Abstract

This paper describes observations of a field of deep and regular cloud formations that spans several hundreds of kilometers at the top of a midlatitude frontal system in the North Pacific storm track. Space-based imagery of the event from active and passive measurements reveals smooth, clearly defined cloud lobes approximately 10 km across and 2–4 km deep that resemble upside-down mammatus. These observations, together with theoretical arguments and prior modeling work, suggest that the lobes were part of a deepening turbulent mixed layer that formed as a consequence of strong cloud-top radiative cooling. Over the course of a day, the cloud-top formation evolved to leave behind a sheet of cumuliform cirrus that stretched hundreds of kilometers across. The potential is for such clouds to facilitate mixing across the tropopause, much as cloud-top cooling drives the entrainment of free-tropospheric air into stratocumulus-topped boundary layers.

1. Introduction

As a consequence of the first and second laws of thermodynamics, all atmospheric processes are slaves to the global requirements that i) incoming and outgoing energy fluxes at the top of the atmosphere (TOA) are in approximate balance and ii) energetic transformations within the Earth’s climate system spread available radiative energy from concentrated high-energy photons within the solar beam into a more-diffuse and/or lower-temperature thermal radiation that is radiated to space. This is accomplished either by the scattering of radiation or through its thermal absorption and emission at progressively colder temperatures.

Atmospheric motions provide an additional mechanism for transporting thermal energy to a colder state. Throughout nearly the entirety of the atmosphere’s depth, air is sufficiently dense to maintain equilibrium between the internal vibrational and rotational modes of molecules that are excited by radiative absorption and the three modes of molecular translational motion that are sensed meteorologically as temperature. The consequence of this equilibrium is that horizontal and vertical radiative flux divergence sets up fluid temperature and pressure gradients that lead to some combination of turbulent and laminar atmospheric flows.

Clouds are optically dense and spatially and temporally intermittent. They provide the atmosphere with an exceptionally efficient means for establishing sharp pressure gradients that may ultimately lead to radiatively driven atmospheric flows. In fact, because the heating and cooling rates in clouds are so rapid compared to those of the surrounding clear skies, such flows often break down into turbulence. The pressure gradients that are established cannot be relaxed through laminar horizontal motions, so vertical mixing develops instead (Schmidt and Garrett 2013). One well-known example is how cloud-top radiative flux divergence maintains broad sheets of boundary layer clouds: cloud-top cooling accelerates condensation and contributes to the production of negatively buoyant air near cloud top, providing a source of energy that sustains boundary layer overturning.

This paper presents a striking case of a deep and periodic cloud structure at the top of a large frontal system along the northwestern Pacific storm track. We argue that the formation arose as a consequence of efficient radiative cooling, which led to the development of a convectively overturning mixed layer several kilometers deep. Remarkably, the layer gives the appearance of a field of mammatus lobes, the pendulous features sometimes observed hanging from the base of stratiform storm clouds (Schultz et al. 2006). What stands out is the very large size of the lobes and the fact that they protrude upward from the cloud top. The suggestion is that these cloudy formations have the potential to facilitate stratospheric–tropospheric exchange through vigorous turbulent mixing.

2. Observations

a. Radar and lidar observations

The data used in this study are derived primarily from active measurements from the 94-GHz Cloud Profiling Radar (CPR) aboard CloudSat (Marchand et al. 2008), the two-wavelength-polarization Cloud–Aerosol Lidar with Orthogonal Polarization (CALIOP), and the Infrared Imager Radiometer (IIR) aboard the Cloud–Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) (Winker et al. 2009) positioned within the A-Train constellation of satellites (Stephens et al. 2002). Level 2B CloudSat geometric profile product (2B-GEOPROF) radar reflectivities are used for analysis of the spatial statistics of the cloud field. CloudSat 2B-GEOPROF lidar data (Mace et al. 2009) are used to assess cloud-top statistics. Thermodynamic variables that we analyze below are part of CALIPSO level 1 ancillary data and come from meteorological reanalyses.

Figure 1a shows a satellite image from 23 December 2008 of a cloud system located approximately 1000 km east of the coast of Japan between the latitudes 28° and 53°N and the longitudes 160° and 168°E. The satellite imagery is a combination of geostationary data provided by the National Centers for Environmental Prediction (NCEP) and Advanced Very High Resolution Radiometer (AVHRR; polar) imagery provided by the National Oceanic and Atmospheric Administration’s (NOAA) Comprehensive Large Array-data Stewardship System (CLASS) [this imagery is available online through the CloudSat data processing center, the Cooperative Institute for Research in the Atmosphere (CIRA): http://www.cloudsat.cira.colostate.edu/dpcstatusQL.php]. A miniature of the cloudy portion of the system from the CPR on the CloudSat platform is visible at the bottom of the figure and covers the CloudSat-referenced segments 27, 28, and 29. The cloud system is oriented southwest to northeast and is approximately 3000 km long and 1000 km wide. Motion of the system is northeastward. Active instruments from the A-Train sampled the cloud system’s width and length seven times between 0223 UTC 22 December and 1421 UTC 24 December. Figs. 1b and 1c show two other geostationary views of the cloud system.

Fig. 1.

Geostationary views of the North Pacific with CloudSat and CALIPSO surface track at around (a) 1520 UTC 23 Dec and (b) 0226 and (c) 1420 UTC 24 Dec 2008.

Fig. 1.

Geostationary views of the North Pacific with CloudSat and CALIPSO surface track at around (a) 1520 UTC 23 Dec and (b) 0226 and (c) 1420 UTC 24 Dec 2008.

The overpass between 1517 and 1526 UTC (0317 and 0326 local time) by the CloudSat platform within the A-Train series of satellites offers a detailed view of the cloud system’s internal structure, from north to south. Figure 2 shows CloudSat CPR radar reflectivities. The horizontal resolution is around 1.5 km, while the vertical resolution is about 500 m; the radar signal is obtained vertically every 240 m, while the altitude at each point has an uncertainty of approximately 230 m. Radar reflectivity ranges between −20 and 20 dBZ.

Fig. 2.

CPR/CloudSat radar reflectivity (dBZ) within sections 27–29 shown in Fig. 1, 23 Dec 2008, between 1517 and 1526 UTC. The red line indicates the cloud upper contour as given by CALIOP. A bright band is visible, which indicates a melting layer of snow. The circle highlights the surface location of a warm-frontal zone.

Fig. 2.

CPR/CloudSat radar reflectivity (dBZ) within sections 27–29 shown in Fig. 1, 23 Dec 2008, between 1517 and 1526 UTC. The red line indicates the cloud upper contour as given by CALIOP. A bright band is visible, which indicates a melting layer of snow. The circle highlights the surface location of a warm-frontal zone.

The upper boundary of the cloud system shown in Fig. 2 is determined by CALIOP, as taken from the CloudSat 2B-GEOPROF lidar product. Just below this upper boundary, CloudSat radar imagery shows a marked internal structure that lies between 34°N, 162°E and 41°N, 164°E. Reflectivities in what appear to be lobes are greater than −10 dBZ, largely above the minimum detectable reflectivity factor of −29 dBZ (the calibration accuracy of the instrument CPR is 1.5 dB, while its dynamic range is 70 dB). Two additional pieces of data—data quality and CPR cloud mask—are included with radar reflectivities. These indicate good data quality, meaning that false detection of cloud-top lobes should not be expected. The confidence in the radar signal is reaffirmed by the remarkable correlation with the lidar backscattered signal. A closer look at this cloud-top region is shown in Fig. 3, which illustrates radar and lidar views between the altitudes of 8 and 14 km. Abscissas are great-circle distances in kilometers obtained from the target’s coordinates, with the origin at the south of the cloud system. The cloud top displays pronounced nearly regularly spaced lobes that protrude upward. The lobe boundaries are apparent from the regions where there is deeper penetration of the lidar within the cloud system and where radar reflectivities are less than −15 dBZ. The cloudy lobes are about 10 km wide and 2–3 km deep. The maximum depth extends to 4 km, for example, around the horizontal location 900 km, where the holes between the lobes extend from a higher top altitude of approximately 13.3 km down to 9.3 km. Assuming that the lobes are part of a turbulent phenomenon, the cell aspect ratio of 3–5 suggests high anisotropy within a gravitationally stratified atmosphere.

Fig. 3.

(a) (bottom) CPR/CloudSat radar reflectivity and (top) CALIOP/CALIPSO lidar total attenuated backscatter at 0.532 μm in the upper part of the cloud system, where regular cloud formations developed. The red line indicates the cloud upper contour as given by CALIOP. The white line indicates the altitude at which the cloud optical depth below the cloud upper contour would equal unity. Abscissas are great-circle distances in kilometers obtained from the target’s coordinates, with the origin at the south of the cloud system. (b) A zoom shot of the area between the abscissas 1180 and 1400 km.

Fig. 3.

(a) (bottom) CPR/CloudSat radar reflectivity and (top) CALIOP/CALIPSO lidar total attenuated backscatter at 0.532 μm in the upper part of the cloud system, where regular cloud formations developed. The red line indicates the cloud upper contour as given by CALIOP. The white line indicates the altitude at which the cloud optical depth below the cloud upper contour would equal unity. Abscissas are great-circle distances in kilometers obtained from the target’s coordinates, with the origin at the south of the cloud system. (b) A zoom shot of the area between the abscissas 1180 and 1400 km.

Cloud classification is traditionally done using the human eye and visible wavelengths. The nearest tool that is available in this case is the CALIOP lidar, and we use it here to compute an “optical” boundary for the cloud that roughly corresponds to what might be seen by the human eye. The integrated optical depth starting at the upper boundary is given by , where ext532 is the extinction coefficient at 532 nm inferred from CALIOP measurements and δz = 60 m is the vertical resolution of CALIOP. We estimate that the depth at which τ equals unity should roughly correspond to the “visible” upper envelope of the cloud-top formation, as indicated in Figs. 3a and 3b by a white line. The envelope also indicates a lobed pattern, although less deep and regular than in the radar returns. For example, for the abscissa 1320, a lobe has a 1.5-km vertical depth between altitudes of 11 and 12.5 km.

Because the features strongly resemble the mammatus lobes that are commonly seen protruding downward from the underside of thick cirrus anvils (Schultz et al. 2006), we refer to them as mammatocumulus. What is unusual in this case is that the lobes extend upward from the cloud top.

b. Meteorological context

The meteorological context has been analyzed using Global Modeling and Assimilation Office (GMAO) and European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis fields. GMAO data (Bloom et al. 2005; Bey et al. 2001) are available with CALIPSO CAL_LID_L2_05kmCPro files and consist of diagnosed temperature, pressure, and humidity fields at the location of each 5-km CALIPSO pixel, vertically interpolated to each lidar-data altitude. Wind and potential vorticity fields are obtained from the ECMWF dataset at a horizontal grid spacing of 0.25° every 6 h and at 12 pressure levels in the troposphere (Dee et al. 2011). A pressure-to-altitude conversion is derived using CALIPSO data. It should be kept in mind that GMAO data are Gridpoint Statistical Interpolation (GSI)-derived data. The GSI system is a variational data assimilation system, so clouds are not explicitly considered. Thus, the temperature field does not explicitly reflect the extent to which cloud processes could have modified local thermodynamic properties, except insofar as they are reflected in more sparse atmospheric soundings.

As shown in Fig. 4, the reanalysis meteorological data describe the presence of a large anticyclone (1035 hPa) in the northwestern Pacific. The cloud system is west of this anticyclone within a quite strong surface wind field, which turns clockwise around it. The meteorological fields within the cloud system evolve slowly between 1200 and 1800 UTC 23 December, implying that the meteorological data from 1200 UTC shown in Fig. 4 and later correspond approximately to the satellite imagery from 1520 UTC. Figure 5 shows the vertical profile of the GMAO thermodynamic and potential temperature fields superimposed on the coincident CloudSat reflectivity profile of the cloud system. On the right side of Fig. 5, the rise and drop of isolines of potential and thermodynamical temperatures, respectively (including the 0°C bright-band near 47.5°N, 166°E), indicate that the cloud system lies along a warm front. The warm front remains evident almost 23 h later (Fig. 12) when active sensors resampled the cloud system at 1420 UTC 24 December. The great-circle distance between the two locations (i.e., their distance over Earth’s surface) is 1861 km, implying an average propagation speed for the front of 22.5 m s−1. ECMWF data indicate similar values for the horizontal surface wind (see Fig. 7). The frontal cloud system follows an upper-tropospheric jet with maximum winds located between 10- and 12-km altitude, as shown in Fig. 6. The wind direction is northeastward (Fig. 6a), reaching 80 m s−1. Figure 7 shows a vertical cross section of the wind field, where in the mammatocumulus region, the horizontal wind is between 30 and 50 m s−1 with positive shear. The presence of shear might account for the tilt of some of the lobes visible in Fig. 3b, particularly near the 1250- and 1350-km horizontal markers. The role of shear in the mammatocumulus production is considered further in the discussion below. The ECMWF-diagnosed vertical wind (color shading on Fig. 7) shows consistency between the location of the cloud system and the area where negative divergence of the horizontal winds leads to upward motion.

Fig. 4.

Temperature field and horizontal wind close to the surface as well as mean sea level pressure from ECMWF data at 1200 UTC 23 Dec 2008. The black line and dots indicate the total and surface horizontal extents of the cloud system seen in CloudSat CPR imagery at 1520 UTC 23 Dec 2008.

Fig. 4.

Temperature field and horizontal wind close to the surface as well as mean sea level pressure from ECMWF data at 1200 UTC 23 Dec 2008. The black line and dots indicate the total and surface horizontal extents of the cloud system seen in CloudSat CPR imagery at 1520 UTC 23 Dec 2008.

Fig. 5.

Vertical profile of temperature field from GMAO reanalysis (white contours; °C) and ECMWF potential temperature (colored shading; K; at 1200 UTC) superimposed on the CloudSat reflectivity signal of the cloud system at 1520 UTC 23 Dec 2008. Red lines show the potential vorticity (PV) from ECMWF for 1, 2, and 3 PVU. The thick horizontal black line indicates the diagnosed tropopause height.

Fig. 5.

Vertical profile of temperature field from GMAO reanalysis (white contours; °C) and ECMWF potential temperature (colored shading; K; at 1200 UTC) superimposed on the CloudSat reflectivity signal of the cloud system at 1520 UTC 23 Dec 2008. Red lines show the potential vorticity (PV) from ECMWF for 1, 2, and 3 PVU. The thick horizontal black line indicates the diagnosed tropopause height.

Fig. 6.

ECMWF horizontal wind (m s−1) for level 8 (10.2 km) at (a) 1200 UTC 23 Dec and (b) 1200 UTC 24 Dec 2008. The black line and dots indicate the total and surface horizontal extents of the cloud system as seen in CloudSat CPR imagery at 1520 UTC 23 Dec and at 1430 UTC 24 Dec 2008. The additional 2D color plot in (a) shows brightness temperatures in the mammatocumulus area obtained from measurements at 10.6 μm from IIR onboard the CALIPSO platform within a 69-km swath. The limits of the color scale given by blue and red are 205 and 230 K, respectively.

Fig. 6.

ECMWF horizontal wind (m s−1) for level 8 (10.2 km) at (a) 1200 UTC 23 Dec and (b) 1200 UTC 24 Dec 2008. The black line and dots indicate the total and surface horizontal extents of the cloud system as seen in CloudSat CPR imagery at 1520 UTC 23 Dec and at 1430 UTC 24 Dec 2008. The additional 2D color plot in (a) shows brightness temperatures in the mammatocumulus area obtained from measurements at 10.6 μm from IIR onboard the CALIPSO platform within a 69-km swath. The limits of the color scale given by blue and red are 205 and 230 K, respectively.

Fig. 7.

Vertical profiles of the horizontal (black contours) and vertical (colored shading) wind speeds (m s−1) at 1200 UTC 23 Dec 2008 taken from the ECMWF reanalysis along the A-Train transect of the cloud system. Profiles superimposed on the CloudSat reflectivity signal of the cloud system at 1520 UTC 23 Dec 2008.

Fig. 7.

Vertical profiles of the horizontal (black contours) and vertical (colored shading) wind speeds (m s−1) at 1200 UTC 23 Dec 2008 taken from the ECMWF reanalysis along the A-Train transect of the cloud system. Profiles superimposed on the CloudSat reflectivity signal of the cloud system at 1520 UTC 23 Dec 2008.

The top of the cloud system observed on 23 December generally lies between 12 and 13.5 km. As shown in Fig. 5, the cloud top pushes up against the tropopause, the altitude of which decreases northward. The examination of the reanalyzed potential vorticity field (red lines on Fig. 5) indicates no characteristic signature of a stratospheric intrusion or tropopause fold or evidence of an upper-level front like in Homeyer et al. (2011) and Luce et al. (2012). Over the mammatocumulus region, however, the tropopause is diagnosed to be 900 m higher than its surroundings, reaching 13.2 km over a 100-km-wide area. Above this region, there is a volume of particularly cold air aloft, with a local temperature of −65°C. While suggestive, any inference of a correlation between this tropopause height anomaly, the locally colder temperature, and the existence of the cloud-top lobes should be considered with caution. Meteorological data do not explicitly consider mesoscale cloud dynamics.

c. Infrared observation

The distinctive mammatocumulus cloud feature is characterized by a highly variable structure with remarkable periodicity and vertical depth in signatures from active sensors. This high “activity” at the top of the cloud system is also apparent in passive infrared observations from the IIR onboard the CALIPSO platform. The IIR instrument measures upward radiances at the wavelengths of 8.65, 10.6, and 12.05 μm within a 69-km swath centered on the lidar track, with a 1 km × 1 km spatial horizontal resolution. The 2D color plot included in Fig. 6a shows brightness temperatures at 10.6 μm deduced from the IIR measurement in this 69-km swath. Blue represents the coldest brightness temperatures (205 K) that correspond to the top of the lobes. Red represents the highest local temperatures (230 K) and corresponds to the deepest gap between lobes. From GMAO data, the local lapse rate is close to the dry adiabatic value at these cold temperatures. The observed brightness temperature difference of 10–20 K in the mammatocumulus region is thus consistent with the altitude depression of 1–2 km determined at visible wavelengths using the lidar.

A 2D color plot of Fig. 6a shows that brightness temperatures and cloud-top formations in the southern part of the mammatocumulus region are less organized than in the northern part, where they seem to be arranged into lines oriented northwest–southeast. These linearly organized cloud formations would be oriented perpendicular to the high-altitude wind shown in Fig. 6. We notice the resemblance of this feature of cloud organization into lines to modeling studies of mammatus clouds in sheared environments (Kanak and Straka 2009) and to cirrus bands close to the jet stream (Knox et al. 2010). Where the mammatocumulus formations are organized into cloud lines, we suggest that they be termed mammatocumulus lucullus.1

d. Cloud structure and periodicity

The spectacular cloud-top formation that we describe here has the remarkable feature of being spatially regular over a large region approximately 700 km wide. To provide an objective assessment of the characteristic spatial scales associated with this unique region, we apply signal processing techniques to the 10.6-μm thermal emission imagery signal of the cloud system, as measured by the IIR instruments on board CALIPSO. First, we use a wavelet-based tool to objectively characterize and assess the location of this area. Then, we perform a Fourier analysis to identify the dominant periodicity of the cloud-top features.

The bottom-right-hand panel of Fig. 8 shows the 1D brightness temperature signal at 10.6 μm over the frontal cloud. It corresponds to the central measurements over the 69-km swath (i.e., on the CloudSatCALIPSO track). We perform first a multiresolution wavelet analysis of this signal. Wavelets have been successfully applied by others for the study of cirrus dynamics and structure (Smith and Jonas 1997; Quante et al. 2002; Wang and Sassen 2008). Here, Meyer functions are used as the wavelet basis because of their mathematical consistency with Fourier spectral decomposition (Ferlay et al. 2006). Figure 8 shows the Meyer-based discrete multiresolution analysis of the brightness temperature signal: it is decomposed into an approximation at the chosen resolution of 256 km (top-left-hand panel of Fig. 8), and into finer and finer details at half resolutions (256, 128, 64 km, etc.) down to 2 km, twice the measurement horizontal resolution. Consequently, the brightness temperature signal plotted on the bottom-right-hand panel of Fig. 8 represents exactly the sum of the signals plotted in the nine other panels. Each detail that is extracted is smooth and well localized in frequency space. In the coarse-scale approximation of the analysis (top-left-hand panel of Fig. 8), the mammatocumulus region is characterized by temperatures colder than 220 K. Temperature variability is largest at spatial scales between 2 and 16 km and in horizontal locations between 800 and 1500 km.

Fig. 8.

Discrete wavelet-based multiresolution analysis of the CALIPSO IIR 10.6-μm brightness temperatures for the cloud system shown in Fig. 2.

Fig. 8.

Discrete wavelet-based multiresolution analysis of the CALIPSO IIR 10.6-μm brightness temperatures for the cloud system shown in Fig. 2.

Within this mammatocumulus region of high variability that has been objectively identified through wavelet analysis, we perform a Fourier transform of the IIR signal and compute the power spectrum of nine IIR 10.6-μm signals that are centered along the CloudSatCALIPSO track and spaced by 1 km orthogonal to the track. This power spectrum is shown by the blue line in Fig. 9. For comparison, the black line illustrates the power spectrum of the IIR measurements observed within the cloudy area outside of the mammatocumulus region. Consistent with the multiresolution wavelet analysis, the energy of the brightness temperature signal is largest within the mammatocumulus portion of the cloud system and over spatial scales ranging between 2 and 50 km. What the Fourier analysis reveals in addition to the wavelet analysis is a significant variability peak at scales near 23 km. High power at this scale can be related directly to the more subjectively assessed periodicity of the cloud-top structures shown in Figs. 2 and 3. Over the intermediate portion of the mammatocumulus power spectrum, the brightness temperature variability has the characteristic −-power-law behavior that is normally associated with an energetic cascade in isotropic turbulence (Tennekes and Lumley 1972). At spatial scales larger than 20 km, the power of the brightness temperature signal shows only very weak dependence on spatial scale. Outside of the mammatocumulus region, however, a slope close to − is maintained up to scales of 100 km. Below a scale break at about 6 km, both signals have a spectral slope of approximately −5. This is indicative of a scale break toward sharply increasing smoothness in cloud features at smaller scales. Figure 9 also shows the power spectra of the radar and lidar signals (red and green lines, respectively), calculated as a vertical average within the mammatocumulus layers. The altitudes for the calculations are between 12.2 and 12.9 km for the lidar signal and between 11.5 and 13.2 km for the radar signal. The spectrum of the 94-GHz (3200 μm) CPR signal is shifted one decade upward on Fig. 9 because it would otherwise overlay the IIR spectra inside the mammatocumulus region (there is similar sensitivity of the infrared and millimeter-wavelength signals to the cloud variability). The one difference is that there is a slightly more pronounced periodicity in the radar signal, with variability maxima at scales of about 23 and 18.5 km. Over the intermediate portion of the spectrum, the radar signal has a spectral slope close to − and a scale break near 6 km. Below this scale, however, the spectral slope is slightly smaller, with a value of approximately −3.5. The power spectrum of the CALIOP 0.532-μm lidar total attenuated backscatter signal shows a 23-km periodicity, although the signal is comparatively weak. Lidar penetrates less deeply into cloud than thermal or radar signals, so it does not “see” as efficiently the deep-lobed structures that are present. At small spatial scales, the spectral slope is close to − but without any scale break.

Fig. 9.

Power spectra of the IIR 10.6-μm brightness temperatures (BT) inside and outside of the mammatocumulus region (denoted MaCu in the legend) of CALIOP total attenuated lidar backscatter (TAB) at 0.532 μm and of CloudSat 94-GHz CPR reflectivity factor inside the mammatocumulus region. For clarity, the CPR spectrum is shifted upward one decade.

Fig. 9.

Power spectra of the IIR 10.6-μm brightness temperatures (BT) inside and outside of the mammatocumulus region (denoted MaCu in the legend) of CALIOP total attenuated lidar backscatter (TAB) at 0.532 μm and of CloudSat 94-GHz CPR reflectivity factor inside the mammatocumulus region. For clarity, the CPR spectrum is shifted upward one decade.

Our interpretation of these results is that the observed scale break depends on sensor wavelength, because there is a size dependence in the inertial response of cloud and precipitation particles to turbulence. Typically, short-wavelength radiation responds most strongly to the smallest particles of a hydrometeor size distribution. Longer thermal wavelengths respond most strongly to the largest cloud particles, and millimeter-wavelength radar responds most strongly to precipitation. It appears that visible, thermal, and microwave signals are all affected equally by the turbulent motions that affect both cloud and precipitation particles, regardless of particle size, but only provided that the spatial scales of the turbulence are larger than 6 km. At scales smaller than 6 km, the radar signal has higher spatial roughness than the thermal signal, and the visible wavelength signal shows no evidence of any scale break while maintaining a spectral slope of −. We infer from these results that small ice particles act as efficient tracers of the smaller-scale turbulent motions to which heavy precipitation particles respond only weakly.

3. Discussion: Formation mechanisms

The observed cloud-top structure is intriguing and raises the question of its formation mechanism. The meteorological data, despite its low resolution, shows broad consistency with satellite measurements. Yet an analysis of the potential vorticity field does not show any tropopause fold and any intrusion of stratospheric air into the troposphere that might lead to an upper-tropospheric increase in convection. The horizontal wind is high in the mammatocumulus area, and there is moderate wind shear (see Fig. 7) but, as we discuss later, the magnitude of shear is insufficient to explain the observed cloud structure. It is unlikely that conditions are met for the onset of Kelvin–Helmholtz instabilities and billows (Luce et al. 2012). Last, there is no apparent source of convective overshooting sufficient to generate a 700-km-wide field of 4-km-deep gravity waves.

Instead, the cloud-top structure that we present looks strikingly like mammatus clouds. Mammatus clouds are among the more intriguing of atmospheric phenomena for their dramatic visual appearance, especially when the sun is low on the horizon and the contrast between pouches is at its highest and most colorful. Normally, mammatus lobes are smooth and regularly spaced, protruding downward from cloud base in visible and radar imagery (Martner 1995; Winstead et al. 2001; Schultz et al. 2006). Here we see mammatus-like structures that protrude instead upward from the cloud top. To our knowledge, this is the first time “upside-down” mammatus has been described in observations.

To examine more closely this cloud-top structure, we analyze retrievals of its properties using the Cloud-Aerosol-Water-Radiation Interactions Center’s radar–lidar project (DARDAR) approach. DARDAR uses a synergetic combination of CloudSat, CALIPSO, and MODIS measurements within a variational framework (Delanoë and Hogan 2008, 2010). Cloud products have a 60-m vertical resolution at the CloudSat horizontal footprint resolution of 1.4 km. Figure 10 shows the DARDAR-estimated cloud ice water content (IWC) in milligrams per cubic meter and ice effective radius re in micrometers in the mammatocumulus region. In the upper part of the cloud, IWC is limited to about 100 mg m−3 and re is limited to about 60 μm. The highest values of IWC are seen locally inside the mammatocumulus lobes at altitudes above 12 km. The observed periodicity in IWC and effective radius is consistent with the lidar and radar profile of the cloud top. Holes in the radar profile are associated with small values of IWC ≤ 40 mg m−3 and values of re around 30 μm. The tilted characteristic of the lobes is clearly visible in the IWC spatial structure at several locations (e.g., at 1250 and 1350 km). So, what we refer to as mammatocumulus can be defined more objectively as high values of IWC and re concentrated into periodic upward-pointing lobes, possibly tilted, where the intervening spaces contain small particles.

Fig. 10.

Retrieved cloud quantities from the DARDAR algorithm in the upper part of the mammatocumulus region: Ice water content is in units of milligrams per cubic meter and the ice crystal effective radius in units of micrometers.

Fig. 10.

Retrieved cloud quantities from the DARDAR algorithm in the upper part of the mammatocumulus region: Ice water content is in units of milligrams per cubic meter and the ice crystal effective radius in units of micrometers.

In general, mammatus clouds have remained somewhat of a puzzle. In a review article, Schultz et al. (2006) provided a history of efforts to describe mammatus and outlined a broad variety of possible explanations. The prevailing theory is that evaporative cooling plays a key role. If the air below a cirrus anvil is dry, precipitation sublimates and enhances development of negatively buoyant cloudy thermals. Numerical simulations have borne out this mechanism as providing the necessary ingredients for mammatus-like clouds, given an appropriate set of initial conditions (Kanak and Straka 2006; Kanak et al. 2008).

In the case presented here, however, sublimation of precipitation cannot be responsible for the upwardly protruding cloudy lobes that we observe. Precipitation falls down, not up. Any evaporative cooling of hydrometeors would propel the cloudy lobes in the wrong direction. Rather, we suggest that the mammatocumulus clouds that we observe might develop instead as a consequence of an instability that is driven by local radiative flux divergence (Garrett et al. 2010; Schmidt and Garrett 2013), much as radiative cooling is seen as a driving force for turbulence at the tops of stratocumulus decks (Lilly 1968; Moeng et al. 1995, 1996). In the case of the large cloud frontal system seen here, the instability is created by longwave radiative cooling to space from the cloud top. Because the tops are at a high altitude and above most of the water vapor blanket that insulates Earth, this thick cloud system emits to space essentially as a blackbody with the temperature of the cloud top TCT. Thermal emission downward from the stratosphere is relatively small. Also, because the cloud is essentially a blackbody, the thermal radiation field is isotropic deeper within the cloud interior. This means that any radiative temperature contrast between the cloud top and the upper atmosphere concentrates radiative cooling to within a thin layer near cloud top, with near-zero radiative heating above and below (Fig. 11). This heating gradient is the engine for a buoyant instability. What follows is a mesoscale circulation that appears to entrain clear air from above the cloud into the cloudy interior. Mammatocumulus are simply the cloudy manifestation of the return circulation. Such radiatively driven entraining circulations have been reproduced numerically, both at cloud bottom and cloud top, and for similar atmospheric conditions to those described here (Garrett et al. 2010; Schmidt and Garrett 2013).

Fig. 11.

Sketch of the proposed mechanism for upside-down mammatus near the top of a large cloud system whose stratiform region has an initial local stability υ/dz > 0. A radiative temperature contrast results in concentrated cooling at rate over a penetration depth h. If the cloud has a sufficient width L, then a turbulent mixed layer develops with depth δz.

Fig. 11.

Sketch of the proposed mechanism for upside-down mammatus near the top of a large cloud system whose stratiform region has an initial local stability υ/dz > 0. A radiative temperature contrast results in concentrated cooling at rate over a penetration depth h. If the cloud has a sufficient width L, then a turbulent mixed layer develops with depth δz.

Garrett et al. (2010) and Schmidt and Garrett (2013) showed how this problem can be viewed theoretically. Calculation of a dimensionless “spreading number” helps to predict the dynamic response of a cloud with finite lateral dimensions when it is heated or cooled at its boundaries:

 
formula

Suppose a cloud that floats within a stably stratified clear-sky environment with characteristic buoyancy frequency N = [g(υ/dz)/θυ]1/2, where θυ is the virtual potential temperature and g is the gravitational acceleration. Radiative flux divergence within the cloud causes a local temperature change at rate υ/dt over a depth of cloud h and a width of cloud L. At the top of a deep convective system with cold tops, can be approximated by the following equation:

 
formula

where is the emission temperature of the cloud top, is the downwelling thermal emission from the stratosphere with radiative temperature , cp is the specific heat capacity, and ρ is the air density. Any feedback associated with latent heating is negligibly small at very cold temperatures (Arakawa and Schubert 1974; Heymsfield and Miloshevich 1991). The e-folding penetration depth for the deposition of thermal radiation into cirrus depth h is given by (e.g., Stephens et al. 1990)

 
formula

where γ is the thermal diffusivity factor for isotropic radiation (~1.7) (Hermann 1980), qi is the ice water mixing, and k(re) is the ice crystal size-dependent mass-specific absorptivity at thermal wavelengths.

In general, low values of < 1 are associated with weak cloud-top cooling and small cloud widths. In this case, pressure perturbations that are created by radiative flux divergence can be returned to equilibrium through gradual subsidence while keeping isentropic surfaces approximately flat. Through continuity, the cloud then spreads outward.

However, if > 1, laminar isentropic flows are insufficiently rapid to restore radiatively developed pressure gradients to equilibrium. Instead, radiative cooling sets up a gravitational instability. A mixed layer develops and lateral spreading takes the form of turbulent density currents. If the value of is particularly large, then mammatus-like cloud features develop in the central part of the cloud base and inverted mammatus features develop in the central portion of the cloud top. Any potential energy that is added to the central portion of the cloud through radiative flux divergence deepens the turbulent mixed layer faster than horizontal pressure gradients can restore gravitational equilibrium through spreading at the cloud edges. The rate at which the mixed layer deepens is

 
formula

or, integrated over time,

 
formula

A more general form of this time dependence is given by Turner (1979), their Eq. (9.2.9), which addresses the response of a mixed layer to heating at a boundary. In Garrett et al. (2010), it was shown in numerical simulations how mammatus lobes are the visible, cloudy portion of the mixed-layer circulations. They develop from an initially quiescent cloud only if values of are greater than about 1000. In general, such conditions are favored by clouds that are broad (meaning large values of L), dense (meaning small values of h), and for which deposition of radiant energy into the cloud is either much lower or higher than the thermal radiant flux out of the cloud (meaning large values of ). Does the case shown here satisfy the condition of > 1000 that appears to be required to initiate mammatus-like cloud formations? The DARDAR retrievals shown in Fig. 10 suggest characteristic values for re and IWC in the cloud-top lobes of 40 μm and 100 mg m−3, respectively. This implies an approximate value for k(re) of 0.03 m2 g−1 (Knollenberg et al. 1993). The turbulent region between 900 and 1400 km in Fig. 3a has a cloud-top pressure of approximately 130 hPa and a temperature of 210 K, implying a local air density of 0.22 kg m−3. Thus, from Eq. (3), thermal radiation is deposited within a cloud absorption depth of h = 1/(1.67 × 0.03 × 0.1) ≃ 200 m.

For the heating rate , radiative fluxes from the CloudSat level 2 “Fluxes and Heating Rates” project (2B-FLXHR) lidar indicate downward and upward fluxes at the cloud top of 20 and 110 W m−2 respectively. Therefore, the energetic loss rate from the cloud is approximately 90 W m−2, and from Eq. (2), this creates a gradient in heating of −176 K day−1 over the 200-m absorption depth. From GMAO reanalyses within the mammatocumulus region, θυ is 332 K and N averages 0.56 × 10−2 s−1 at altitudes between 10 and 11.5 km. An estimate of the width of the turbulent mammatocumulus cloud-top region is L = 700 km. Thus, from Eq. (1), the approximate value of is 6000.

Of course, this estimate of is only approximate because it is based in part on reanalysis estimates of thermodynamic parameters. Nonetheless, numerical simulations described in Garrett et al. (2010) suggest that this value of is more than sufficient to be associated with a rapidly deepening mixed layer and mammatus cloud formation. Equation (5) suggests that it should take only about 2 h to develop a 2-km mixed layer similar to that which is observed, at which point, from Eq. (4), the layer would continue to deepen at a rate of about 30 cm s−1.

Wind shear can act as an additional contributing factor for mixed-layer deepening, and moderate wind shear can even help organize mammatus lobe features into convective rolls (Kanak and Straka 2009). One way to evaluate the relative contributions of shear and buoyancy to turbulence generation is to calculate the local value of the Richardson number within the layer, as defined by Ri = N2/[(dU/dz)2 + (dV/dz)2], where U and V represent the horizontal wind speeds. Values of Ri > 0.25 have a static stability that is too high for shear-generated turbulence to dominate the local flow (Emanuel 1994). While we do not have direct measurements of the local wind shear in the mammatocumulus region, interpolated ECMWF reanalysis data from Fig. 7 provide a vertical profile of the horizontal wind speeds at 1200 UTC 23 December, 3.5 h prior to the A-Train overpass. The wind profile appears to be very steady at this location between 1200 and 1800 UTC. From this vertical profile, we obtained for [(dU/dz)2 + (dV/dz)2] a value of around 5 × 10−5 s−2, with low variability within the mammatocumulus area. Compared to the observed range of values for N2, implied values for the Richardson number are approximately 0.63. This suggests that shear is very unlikely to have played a dominant role in the mixed-layer development.

Regarding the aspect ratio and periodicity of the mammatocumulus lobes, there are obvious similarities here to the Rayleigh–Bénard convection that can be driven by an externally imposed vertical temperature gradient (Müller and Chlond 1996). A characteristic lobe separation of 20 km suggests that the upward component of the Bénard-like cells has a 10-km horizontal dimension. Lobe heights range from 1.5 to 3 km in the radar and lidar data, suggesting an aspect ratio between 3 and 7. Similar aspect ratio values have been observed in the planetary boundary layer and in laboratory-scale flows (Cieszelski 1998).

4. Conclusions

This study has identified an unusual cloud formation at the top of a large frontal cloud system within the North Pacific storm track. In active 94-GHz space-based radar imagery, the features bear a remarkable resemblance to mammatus clouds, with the notable exception that the cloudy lobes protrude upward rather than descending downward. We term these lobes mammatocumulus for their resemblance in shape to mammatus.

The formation mechanism for mammatus clouds that is often provided is one that starts with an initial instability at the cloud base where air has become gravitationally loaded by precipitation (Kanak et al. 2008). Because they point upward, the mammatocumulus lobes that are described here cannot be due to this mechanism. Instead, an alternative explanation appears to be at play where the instability is driven by powerful longwave radiative flux divergence at cloud top. If a cold cloud is especially broad and dense, then theoretical and numerical arguments suggest that the rapid cloud-top radiative cooling will drive downward-descending clear air to create a turbulent mixed layer; cloudy features in the upwelling component of the resulting circulations resemble mammatus lobes (Garrett et al. 2010; Schmidt and Garrett 2013). In addition to their direction, what is notable in the case described here is that the observed lobes are remarkably large, with a characteristic width of about 10 km and a height of between 1.5 and 3 km.

Such clouds may be more than just a dramatic example of interactions between radiation, clouds, and atmospheric dynamics. Figure 12 shows a CloudSat CPR transect of the frontal cloud system 1 day later as it progressed northeastward (see Fig. 1c). Mammatocumulus features continue to be evident at the frontal system top. However, there appear to be regions where the lower portion of the cloud system has entirely decayed, above which the mammatocumulus features have lingered as a cirrocumulus deck that is several hundreds of kilometers in horizontal extent.

Fig. 12.

CPR/CloudSat radar reflectivity (dBZ) of the cloud system at 1421 UTC 24 Dec 2008. The red line indicates the cloud upper contour as given by CALIOP. (a) The entire cloud system. (b) An enhanced horizontal and vertical zoom shot on the lobe structure; abscissas are great-circle distances in kilometers to an origin located west of the cloud system.

Fig. 12.

CPR/CloudSat radar reflectivity (dBZ) of the cloud system at 1421 UTC 24 Dec 2008. The red line indicates the cloud upper contour as given by CALIOP. (a) The entire cloud system. (b) An enhanced horizontal and vertical zoom shot on the lobe structure; abscissas are great-circle distances in kilometers to an origin located west of the cloud system.

A full explanation for this cloud evolution might best be addressed using a numerical model. What these observations suggest is that the radiative forces that initially created the mammatocumulus mixed layer were long lived and that they continued to sustain cellular features long after the parent cloud had disappeared. If so, mammatocumulus clouds might ultimately be linked to an exchange of air between the troposphere and stratosphere (Holton et al. 1995).

An analogous phenomenon could be mixing across a stratocumulus-topped boundary layer where cloud-top radiative cooling drives both boundary layer turbulence and cloud-top entrainment (Lilly 1968; Moeng et al. 1995). Sometimes such entrainment creates deep holes of free-tropospheric dry air that penetrate hundreds of meters into the stratocumulus interior (Gerber et al. 2005). The tops of stratocumulus tend not to be as smooth as mammatocumulus, but this may only be because the feedback from latent heat release becomes negligible at very cold temperatures (Heymsfield and Miloshevich 1991). With mammatocumulus and stratocumulus, however, a broad, dense cloud layer radiates efficiently into relatively dry air aloft. This creates turbulence, entrainment, and mixing along an interface between two distinct atmospheric layers.

The possibility of such an exchange between the troposphere and stratosphere might be considered less important if the observed cloud structure were very rare, but this is almost certainly not the case. In fact, a very similar example of this cloud-top structure was seen on the same day between 1457 and 1500 UTC to the southeast of Greenland (Fig. 13).

Fig. 13.

CPR/CloudSat radar reflectivity (dBZ) of a midlatitude frontal system in the North Atlantic to the southeast of Greenland. The time of the image is between 1457 and 1500 UTC 23 Dec 2008.

Fig. 13.

CPR/CloudSat radar reflectivity (dBZ) of a midlatitude frontal system in the North Atlantic to the southeast of Greenland. The time of the image is between 1457 and 1500 UTC 23 Dec 2008.

Acknowledgments

We thank four anonymous reviewers for their contributions to the manuscript and Sylvie Malardel for helpful discussions about meteorology. This study was supported by CNES through the French research program Terre, Océan, Surfaces continentales, Atmosphère (TOSCA). We are grateful to the ICARE centre (http://www.icare.univ-lille1.fr/) and to Météo-France for providing access to CALIPSO, CloudSat, DARDAR, and ECMWF data, respectively.

REFERENCES

REFERENCES
Arakawa
,
A.
, and
W. H.
Schubert
,
1974
:
Interaction of a cumulus cloud ensemble with the large-scale environment, Part I
.
J. Atmos. Sci.
,
31
,
674
701
, doi:.
Bey
,
I.
, and Coauthors
,
2001
: Global modeling of tropospheric chemistry with assimilated meteorology: Model description and evaluation. J. Geophys. Res.,106, 23 073–23 095, doi:.
Bloom
,
S.
, and Coauthors
,
2005
: Documentation and validation of the Goddard Earth Observing System (GEOS) Data Assimilation System–Version 4. NASA Tech. Rep. NASA/TM–2005–104606, 165 pp. [Available online at http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050175690.pdf.]
Cieszelski
,
R.
,
1998
: A case study of Rayleigh-Bénard convection with clouds. Bound.-Layer Meteor.,88, 211–237, doi:.
Dee
,
D. P.
, and Coauthors
,
2011
:
The ERA-Interim reanalysis: Configuration and performance of the data assimilation system
.
Quart. J. Roy. Meteor. Soc.
,
137
,
553
597
, doi:.
Delanoë
,
J.
, and
R. J.
Hogan
,
2008
: A variational scheme for retrieving ice cloud properties from combined radar, lidar, and infrared radiometer. J. Geophys. Res.,113, D07204, doi:.
Delanoë
,
J.
, and
R. J.
Hogan
,
2010
:
Combined CloudSat-CALIPSO-MODIS retrievals of the properties of ice clouds
.
J. Geophys. Res.
,
115
,
D00H29
, doi:.
Emanuel
,
K. A.
,
1994
: Atmospheric Convection. Oxford University Press, 580 pp.
Ferlay
,
N.
,
H.
Isaka
,
P.
Gabriel
, and
A.
Benassi
,
2006
:
Multiresolution analysis of radiative transfer through inhomogeneous media. Part II: Validation and new insights
.
J. Atmos. Sci.
,
63
,
1213
1230
, doi:.
Garrett
,
T. J.
,
C. T.
Schmidt
,
S.
Kihlgren
, and
C.
Cornet
,
2010
:
Mammatus clouds as a response to cloud-base radiative heating
.
J. Atmos. Sci.
,
67
,
3891
3903
, doi:.
Gerber
,
H.
,
G.
Frick
,
S. P.
Malinowski
,
J-L.
Brenguier
, and
F.
Burnet
,
2005
:
Holes and entrainment in stratocumulus
.
J. Atmos. Sci.
,
62
,
443
459
, doi:.
Hermann
,
G. F.
,
1980
:
Thermal radiation in Arctic stratus clouds
.
Quart. J. Roy. Meteor. Soc.
,
106
,
771
780
, doi:.
Heymsfield
,
A. J.
, and
L. M.
Miloshevich
,
1991
:
On radiation and latent heat feedback in clouds: Implications and a parameterization
.
J. Atmos. Sci.
,
48
,
493
496
, doi:.
Holton
,
J. R.
,
P. H.
Haynes
,
M. E.
McIntyre
,
A. R.
Douglass
,
R. B.
Rood
, and
L.
Pfister
,
1995
:
Stratosphere–troposphere exchange
.
Rev. Geophys.
,
33
,
403
439
, doi:.
Homeyer
,
C. R.
,
K. P.
Bowman
,
L. L.
Pan
,
M. A.
Zondlo
, and
J. F.
Bresch
,
2011
: Convective injection into stratospheric intrusions. J. Geophys. Res.,116, D23304, doi:.
Kanak
,
K. M.
, and
J. M.
Straka
,
2006
:
An idealized numerical simulation of mammatus-like clouds
.
Atmos. Sci. Lett.
,
7
,
2
8
, doi:.
Kanak
,
K. M.
, and
J. M.
Straka
,
2009
:
Effects of linear, ambient wind shear on simulated mammatus-like clouds
.
Atmos. Sci. Lett.
,
10
,
226
232
, doi:.
Kanak
,
K. M.
,
J. M.
Straka
, and
D. M.
Schultz
,
2008
:
Numerical simulation of mammatus
.
J. Atmos. Sci.
,
65
,
1606
1621
, doi:.
Knollenberg
,
R. G.
,
K.
Kelly
, and
J. C.
Wilson
,
1993
:
Measurements of high number densities of ice crystals in the tops of tropical cumulonimbus
.
J. Geophys. Res.
,
98
,
8639
8664
, doi:.
Knox
,
J. A.
,
A.
Scott Bachmeier
,
W.
Michael Carter
,
J. E.
Tarantino
,
L. C.
Paulik
,
E. N.
Wilson
,
G. S.
Bechdol
, and
M. J.
Mays
,
2010
:
Transverse cirrus bands in weather systems: A grand tour of an enduring enigma
.
Weather
,
65
,
35
41
, doi:.
Lilly
,
D. K.
,
1968
:
Models of cloud-topped mixed layers under a strong inversion
.
Quart. J. Roy. Meteor. Soc.
, 94, 292–309, doi:.
Luce
,
H.
, and Coauthors
,
2012
: Kelvin–Helmholtz billows generated at a cirrus cloud base within a tropopause fold/upper-level frontal system. Geophys. Res. Lett.,39, L04807, doi:.
Mace
,
G. G.
,
Q.
Zhang
,
M.
Vaughan
,
R.
Marchand
,
G.
Stephens
,
C.
Trepte
, and
D.
Winker
,
2009
: A description of hydrometeor layer occurrence statistics derived from the first year of merged Cloudsat and CALIPSO data. J. Geophys. Res., 114, D00A26, doi:.
Marchand
,
R.
,
G. G.
Mace
,
T.
Ackerman
, and
G.
Stephens
,
2008
:
Hydrometeor detection using CloudSat—An earth-orbiting 94-GHz cloud radar
.
J. Atmos. Oceanic Technol.
,
25
,
519
533
, doi:.
Martner
,
B. E.
,
1995
:
Doppler radar observations of mammatus
.
Mon. Wea. Rev.
,
123
,
3115
3121
, doi:.
Moeng
,
C.-H.
,
D. H.
Lenschow
, and
D. A.
Randall
,
1995
:
Numerical investigations of the roles of radiative and evaporative feedbacks in stratocumulus entrainment and breakup
.
J. Atmos. Sci.
,
52
,
2869
2883
, doi:.
Moeng
,
C.-H.
, and Coauthors
,
1996
:
Simulation of a stratocumulus-topped planetary boundary layer: Intercomparison among different numerical codes
.
Bull. Amer. Meteor. Soc.
,
77
,
261
278
, doi:.
Müller
,
G.
, and
A.
Chlond
,
1996
:
Three-dimensional numerical study of cell broadening during cold-air outbreaks
.
Bound.-Layer Meteor.
,
81
,
289
323
, doi:.
Quante
,
M.
,
G.
Teschke
,
M.
Zhariy
,
P.
Maaß
, and
K.
Sassen
,
2002
: Extraction and analysis of structural features in cloud radar and lidar data using wavelet based methods. Proc. Second European Conf. on Radar Meteorology, Delft, Netherlands, European Meteorological Society,
95
103
.
Schmidt
,
C. T.
, and
T. J.
Garrett
,
2013
:
A simple framework for the dynamic response of cirrus clouds to local diabatic radiative heating
.
J. Atmos. Sci.
,
70
,
1409
1422
, doi:.
Schultz
,
D. M.
, and Coauthors
,
2006
:
The mysteries of mammatus clouds: Observations and formation mechanisms
.
J. Atmos. Sci.
,
63
,
2409
2435
, doi:.
Smith
,
S. A.
, and
P. R.
Jonas
,
1997
:
Wavelet analysis of turbulence in cirrus clouds
.
Ann. Geophys.
,
15
,
1447
1456
, doi:.
Stephens
,
G. L.
,
S.-C.
Tsay
,
P. W.
Stackhouse
Jr.
, and
P. J.
Flatau
,
1990
:
The relevance of the microphysical and radiative properties of cirrus clouds to climate and climatic feedback
.
J. Atmos. Sci.
,
47
,
1742
1754
, doi:.
Stephens
,
G. L.
, and Coauthors
,
2002
:
The CloudSat mission and the A-Train: A new dimension of space-based observations of clouds and precipitation
.
Bull. Amer. Meteor. Soc.
,
83
,
1771
1790
, doi:.
Tennekes
,
H.
, and
J. L.
Lumley
,
1972
: A First Course in Turbulence. The MIT Press, 300 pp.
Turner
,
J. S.
,
1979
: Buoyancy Effects in Fluids. Cambridge University Press, 368 pp.
Wang
,
L.
, and
K.
Sassen
,
2008
:
Wavelet analysis of cirrus multiscale structures from lidar backscattering: A cirrus uncinus complex case study
.
J. Appl. Meteor. Climatol.
,
47
,
2645
2658
, doi:.
Winker
,
D. M.
,
M. A.
Vaughan
,
A.
Omar
,
Y.
Hu
,
K. A.
Powell
,
Z.
Liu
,
W. H.
Hunt
, and
S. A.
Young
,
2009
:
Overview of the CALIPSO mission and CALIOP data processing algorithms
.
J. Atmos. Oceanic Technol.
,
26
,
2310
2323
, doi:.
Winstead
,
N. S.
,
J.
Verlinde
,
S. T.
Arthur
,
F.
Jaskiewicz
,
M.
Jensen
,
N.
Miles
, and
D.
Nicosia
,
2001
:
High-resolution airborne radar observations of mammatus
.
Mon. Wea. Rev.
,
129
,
159
166
, doi:.

Footnotes

1

Lucullus was a successful Roman general and a reputed gourmand. Lucullus is also an eponymous French delicacy made from very thin alternating layers of smoked beef tongue and foie gras that has the appearance of these clouds when sliced.