1. Introduction

Fair-weather cumuli are fundamental in regulating the vertical structure of water vapor and entropy in the lowest 2 km of the earth's atmosphere over vast areas of the oceans. Thus the effects of these small-scale circulations must be parameterized in large-scale models (Tiedke et al. 1989). Consequently, entrainment and precipitation processes as they relate to updraft and downdraft circulations in the boundary layer clouds are critical for even the most simplified and highly idealized cloud models. Furthermore, detailed observations of the updraft and downdraft structures in fair-weather cumuli are needed to evaluate high-resolution cloud model simulations (e.g., Grabowski and Clark 1993; Grabowski 1995) and the realism of convective elements resolved in large-eddy simulation models of the trade wind boundary layer (e.g., Cuijpers and Duynkerke 1993).

The detailed structure of fair-weather cumuli has been the subject of some of the earliest aircraft studies of cloud microphysics and dynamics (e.g., Squires 1958; Warner 1955). Blyth (1993) provides an excellent review of the conceptual model that evolved from early aircraft measurements of cumulus clouds and describes how that model has mostly remained intact even if more reliable and accurate in situ observations have become available. However, uncertainty remains about the mechanics of the entrainment and precipitation processes and how these processes relate to updraft and downdraft structures (Cotton and Anthes 1989; Blyth 1993; Paluch and Knight 1986; Beard and Ochs 1993).

All in situ aircraft studies of fair-weather cumuli suffer from a major shortcoming—an inability to define instantaneous in-cloud vertical structures (Warner 1977). However, definition of the vertical structure is critical since entrainment and precipitation processes are intimately connected to cloud updraft and downdraft structures. Although aircraft penetrations yield a detailed description of the clouds' horizontal structure, their vertical structure can only be observed by making multiple passes at different heights. This approach is limited because of the relatively short lifetime of the clouds and their inherent spatial and temporal variability. Therefore, since the clouds vary in time and space, much of the vertical structure of fair-weather cumuli is inferred rather than directly measured. Warner (1977) addresses some of the fundamental limitations in using aircraft to study small cumuli. Despite the shortcomings of studies based on in situ measurements, considerable knowledge and understanding has been obtained from these studies by compiling statistics from multiple cloud penetrations (e.g., Warner 1969, 1970, 1973; Paluch et al. 1996), developing case studies (Blyth and Latham 1985), and applying novel thermodynamic analysis techniques (Paluch 1979; Betts 1982).

Kitchen and Caughey (1981) overcome some of the limitations of aircraft observations by using a tethered balloon to study the fine structure in fair-weather cumulus cloud. These observations, made with limited vertical resolution, provided understanding of the vertical structure of circulations associated with the clouds they studied.

Aircraft observations in small cumuli indicate that the cloud liquid water content is often well below theoretical estimates and that vertical velocities fluctuate substantially across their horizontal dimension. Downdrafts observed at the edges of the cloud have been attributed to evaporative cooling caused by mixing with the environmental air. These observational results were consistent with the idea that the principal mechanism responsible for the mixing of clouds with their environment is through cloud-top rather than lateral entrainment. To date, little has been learned that substantially changes these early results, although several recent studies indicate the existence of parcels undiluted by entrainment at all levels inside the clouds (Blyth 1993).

Surface-based remote sensing systems provide the potential for increasing our observational database for the understanding of small cumuli structures. Millimeter-wavelength radars are particularly suitable for the observation of weak meteorological targets such as shallow cumulus clouds since they are far more sensitive than centimeter wave radars for the observation of cloud, because of the 1/λ⁴ (where λ is wavelength) increase of the droplets' backscattering cross section (Rayleigh scattering) (Lhermitte 1987a). Since cloud droplets in a fair-weather cumulus can be considered as Rayleigh scatterers, the millimeter-wavelength radar is an excellent tool for their detection.

Lhermitte (1987b) first demonstrated the capability of 94-GHz millimeter-wavelength radar for the study of fair-weather cumuli structure. During the past 10 years these short-wavelength radars have been used also to study the properties of boundary layer clouds and the processes that affect those properties (Frisch et al. 1995a,b; Clothiaux et al. 1995; Kropfli et al. 1995). Further, millimeter-wavelength radars have been used to define cloud structure internal circulations in stratocumulus clouds (Vali et al. 1998; Wilczak et al. 1996; Kollias and Albrecht 2000) and the structure of cumulus extending into stratus (Miller and Albrecht 1995). However, beyond the initial work of Lhermitte (1987b), there has been relatively little application of millimeter-wavelength radars to study fair-weather cumulus clouds. A millimeter-wavelength radar mounted on the Wyoming King Air was used during the Small Cumulus Microphysics Study (SCMS) to study the time evolution of small cumuli (French et al. 1999). Radars operating at much longer wavelengths are also effective for the study of some aspects of shallow cumuli using Bragg scattering returns (Rogers et al. 1993). During SCMS and earlier during the Convection and Precipitation/Electrification (CaPE) experiment a radar operating at 5- and 10-cm wavelengths (National Center for Atmospheric Research CP-2) was used to study the pre-precipitation stages of cumuli with tops near 3–3.5 km (Knight and Miller 1993; Cooper et al. 1996). Knight and Miller (1998) considered the relative contributions of Bragg and Rayleigh scattering at the two CP-2 wavelengths to study the evolution of cumuli as they approached the precipitation stage.

In the study reported here, we use a 3-mm-wavelength Doppler radar to study the internal circulations in fair-weather cumuli. The radar is capable of detecting weak targets (−45 dBZ at 1 km) and thus can measure the relatively weak returns from cumulus clouds. Real-time processing of the radar signals provides Doppler spectra. The radar is operated in a vertically pointing beam mode to study the vertical structure of updraft and downdraft structures in the clouds—features that have been difficult to observe directly using aircraft observations. Doppler spectra from the radar are used to examine turbulence within the radar sampling volume and to study mechanisms responsible for the growth of large droplets. Concurrent observations from a 915-MHz wind profiler are used to define some aspects of the environment surrounding the clouds and to identify areas of turbulence in the clouds from Bragg scattering returns. In the final section of this paper we will consider how the observed updraft, downdraft, and turbulence structures in the clouds agree with previous in situ aircraft observations and the conceptual model that evolved from these observations.

2. Instrumentation and data processing

c. Bragg versus Rayleigh scattering

UHF wind profilers are sensitive to echoes from “clear air” due to turbulent scales near λ/2, where λ is the wavelength (32.8 cm). These turbulent scales are associated with inhomogeneities of the temperature and moisture field, leading to the index of refraction time and space variability that produces backscattering. These anomalies of the index of refraction lead to partial superimposed reflections of the transmitted power back to the receiver. The return signal intensity can be used for indirect mapping of the turbulent field under the assumption that the variations in the temperature and moisture are of the order of λ/2 (Knight and Miller 1993; Knight and Miller 1998). Moreover, the index of refraction irregularities are moving with the mean wind flow, resulting in mapping of the wind field using the Doppler frequency shift. Using the assumption that one-half of the radar wavelength is within the inertial subrange, the scattering cross section η (m⁻¹) can be expressed as (Balsley and Gage 1982)

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where C²_n (m^−2/3) is the refractive index structure function. The observed Doppler spectrum is the density distribution of the return power as a function of the Doppler frequency shift. The recorded moments of the power Doppler spectrum are used for mapping the boundary layer structure. In terms of signal-to-noise ratio (SNR) units, the boundary layer power returns are coming from the height of the capping inversion, due to strong moisture and temperature gradients; the subcloud layer, due to strong surface moisture fluxes; and from the overpassing clouds. Enhanced returns from nonprecipitating clouds are localized in the cloud boundaries due to strong moisture gradients, especially at the locations where the cloud top penetrates the capping inversion.

Radars operating at 3 mm are the shortest-wavelength radars used in radar meteorology. At this wavelength, the Rayleigh approximation is valid only for small cloud droplets and light drizzle conditions. If the hydrometeors are larger than 500 μm, the more complex Mie scattering functions must be used. The droplet diameters in nonprecipitating shallow cumulus are generally much smaller than the radar wavelength (λ = 3.2 mm). Therefore, Rayleigh scattering is the principal scattering mechanism contributing to the observed backscattering intensities, although the presence of even a few larger droplets may substantially increase the radar reflectivity. Within the Rayleigh approximation for spherical particles the radar reflectivity is

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where η (m⁻¹) is the scattering cross section per unit volume, and |K|² is a function of the complex index of refraction, and Z is the radar reflectivity factor, which is commonly expressed in dBZ. At 94 GHz and a temperature of 20°C the parameter |K|² = 0.828.

Operating at a wavelength of 32.8 cm, the wind profiler detects Bragg scattering and therefore provides observations complementary to the Rayleigh scattering targets observed by the MCR. Due to the relatively small droplets in the clouds observed, it is unlikely that Rayleigh scattering contributes substantially to the observed radar reflectivities from the wind profiler.

3. Interpretation of Doppler radar signals

Although the Doppler spectrum is needed to capture the entire targets' radial velocity statistics and to identify spurious frequency components, spectral moments can provide a large part of the Doppler information useful for the assessment of kinematic conditions in the cloud. These are the first moment (in short, mean Doppler) and the second central moment or spectral variance (called spectrum width in the text). The zeroth moment is the signal mean power and relates to cloud or precipitation radar reflectivity. In the cloud study presented here, these quantities are mapped in height–time coordinates.

For the cloud radar observations used in this study, we expect most of the cloud drops to have diameters between ≈5 and 40 μm. Two important considerations prevail in this case: one, the droplets' backscattering is in the Rayleigh region—that is, their backscattering cross section is proportional to D⁶/λ⁴—and two, the droplets' terminal velocity is negligible compared with vertical air velocity and turbulence. Observations made with a vertically pointing beam relate to the droplets' vertical velocity, that is, the sum of terminal velocity and vertical air speed. The terminal velocity of a cloud droplet is small (0.3 and 7 cm s⁻¹ for a 10- and a 50-μm droplet, respectively), so that the droplets' vertical velocity is primarily due to air motion and turbulence. Doppler spectrum moment calculations require preliminary manipulations of the spectrum such as frequency shifting and noise thresholding.

The first moment can be mapped in time–height coordinates, where time can be considered as an horizontal coordinate assuming simple translation of the cloud at the mean wind speed and no evolution of the cloud internal circulation during the observation time (a few minutes). This procedure reveals the cloud internal circulation structure in terms of updrafts and downdrafts, which we will use to analyze the internal dynamics and the interaction between the cloud and its environment.

The cloud droplets' inertia is small, so they are good tracers of turbulent air velocity in the same way that smoke particles reveal turbulent eddies in a smoke-filled room. Due to their convective nature, fair-weather cumuli are highly turbulent. Thus observations of turbulence intensity (e.g., dissipation rate ε) inside the cloud can be very useful in defining the field of kinetic energy dissipation in the cloud and its relation to the mean velocity field, or more precisely the mean velocity gradients.

The occurrence of air turbulence creates a broadening of the droplets' velocity distribution in the scattering volume. This in turn results in an increase of the spectrum width or variance. Measurement of spectrum width is thus an essential tool in the interpretation of Doppler data in terms of cloud dynamics and cloud interaction with the environment. The most appropriate way to observe and measure Doppler spectrum width is to perform a Fourier transform on the I and Q signals and to calculate the second central moment of the processed spectrum. The noise appears as a baseline in the spectrum and must be removed by thresholding the spectral density. Knowledge of the entire Doppler spectrum also allows us to track some important spectrum features such as bimodality and to identify spurious components that can be eliminated in data editing.

In still air, the first term in Eq. (3) is dominant for raindrops in stratiform rain conditions, which allows the raindrop size distribution to be retrieved from the Doppler spectrum assuming no significant air motion contribution. In the case of cloud droplets, however, the velocity spread due to air motion space and time variability will usually dominate.

For the vertically pointing beam operation, the most important contribution of shear to the spectral broadening is the air vertical velocity variation, Δw, moving horizontally across the beam. A variation of 2 m s⁻¹ across the beam cross section, which is likely to happen in a fair-weather cumulus, will create a very large spectrum variance (σ²_s ≈ 1600 cm² s⁻²). However, for the expected spread of the droplets' terminal velocities (0.3 to 8 cm s⁻¹, see above), the associated Doppler spectrum variance will be only a few cm² s⁻². If the vertical velocity shear is concentrated in a region smaller than the beam cross section, a bimodal spectrum will be created. For relatively wide spectra, spectrum bimodality indicates the presence of sharp vertical velocity gradients such as those in the region between adjacent updrafts and downdrafts (Heymsfield 1976).

The variance due to air turbulence, σ²_t, arises from small-scale variability, in both time and space, of the velocity field within the sampling volume. Air turbulence is a stochastic process that, if there are no boundaries, can be considered as an homogeneous process of turbulent energy dissipation characterized by a dissipation rate ε. Within these assumptions, the turbulence spectrum S(k) has the form

Skaε^2/3k^−5/3(5)

where α is a constant, k is a wavenumber, k = 2π/L, and L is a space scale. The velocity variance is derived from an integral over the turbulent spectrum between k₁ = 2π/L₁ and k₂ = 2π/L₂, which is expressed by

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The small scale L₂ ultimately is limited to λ/2 (λ is the radar wavelength), the smallest scale that can be probed by the Doppler radar. For a snapshot of the velocity field inside the scattering volume, the larger scale L₁ relates to the scattering volume dimension, but for the actual case of a finite dwell time of the signal from which the spectrum is calculated, it also includes large eddies traveling through the sampling volume. In the case of homogeneous turbulence, if both k₁ and k₂ can be clearly identified and if they are both in the inertial subrange, σ²_t can be determined and ε can be derived from the integral above. The transition from inertial subrange to molecular dissipation range occurs at the Kolomgorov microscale l_k given by (Tennekes and Lumley 1972)

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where ν_f is the fluid kinematic viscocity and ε is the dissipation rate. So, the characteristic Kolmogorov scale is a function of the dissipation rate. For typical values of dissipation rate it can reach 1 mm for very low ε values, a value near the λ/2 radar limit, which can thus be safely considered as the smallest scale L₂. However, we must recall that steep velocity gradients in the cloud, in addition to contributing to spectrum width, will drive local air turbulent conditions far from the homogeneous turbulence case and may be the main source of turbulence (shear flow turbulence). Even if the shear contribution to variance is removed and the contribution from air turbulence is determined with confidence, its quantitative interpretation in terms of ε must be done very cautiously. Even with these limitations, it remains that the field of σ²_t within the cloud boundaries is a very valuable indication of the way the kinetic energy dissipation is distributed within the cloud and its relation to the mean flow. In the data presented here, estimates of ε are performed inside the interior of the updraft core, away from shear zones.

4. Meteorological conditions

During the winter and spring of 1999, the 94-GHz radar and the wind profiler were used to observe several shallow cumulus clouds. Observing shallow cumuli at vertical incidence is difficult due to the low probability that a cloud will pass directly overhead. Despite this problem, several cumulus clouds were observed and were classified as either passive or active according to the intensity of their internal kinematics derived from the in-cloud Doppler velocity measurements.

Here, we present observations of two active shallow cumuli made on 29 January 1999 around 0900 local time. The radars were operated from a site a few hundred meters north of the Rosenstiel School of Marine and Atmospheric Science (RSMAS) campus at Virginia Key, Miami, FL (Fig. 1). The synoptic conditions were favorable for the development of shallow cumuli with weak anticyclonic conditions and a sharp inversion that was well defined by the Miami rawinsondes and SNR values from the 915-MHz wind profiler. A surface high pressure system centered northeast of Florida resulted in a southeasterly flow in the boundary layer.

The evolution of the inversion that caps the boundary layer was well defined by the wind profiler SNR (Fig. 2), from 0700 LST (1200 UTC) to 1900 LST (2400 UTC). The height of the capping inversion, indicated by regions of high radar returns, increases nearly linearly with time from 1.6 to 2.0 km during this period. Potential temperature and mixing ratio profiles from the Miami soundings made at the beginning and the end of the observing period (Fig. 3) indicate inversion heights similar to those from the profiler SNR and show temperature and moisture structures that are typical of the trade wind boundary layer. The potential temperature increase and mixing ratio decrease across the inversion are about 6 K and 7–8 g kg⁻¹, respectively. Apart from the inversion height increase during the period of observations, there is relatively little change in the thermodynamics below the inversion, although later in the day, the boundary layer structure 10 km inland becomes slightly warmer and drier than it was during the morning.

During the 14 h of profiler SNR observations shown in Fig. 2, several shallow cumuli that penetrate about 150 m into the capping inversion are marked by an enhanced SNR at the inversion associated with enhanced radar returns extending lower into the boundary layer. There is another relative maximum in the 915-MHz radar SNRs at 800–1200 m that may be associated with a slightly stable layer that caps the more turbulent air in the subcloud layer. Although this layer is not resolved by the low-resolution (significant and standard levels) Miami soundings, such a layer is typical of the trade wind boundary layer. The lifting condensation level (LCL) of surface air at a 15-m height (also shown in Fig. 2) corresponds roughly to the lower SNR maximum at the midlevel of the boundary layer. Many of the fair-weather cumuli returns found during this observing period extend from this layer to the stronger capping inversion near 2-km height. The height of this layer and the LCL calculated from the surface temperature T and specific humidity q show little variation from 1000 to 2200 UTC. Thus, the depth of the cloud layer increased during the same time period.

In this paper we focus on the two shallow cumuli observed around 0900 LST (see the boxed area shown in Fig. 2). These clouds were selected because their centers passed directly over the radar site. Profiles of wind speed and direction from the profiler averaged for 40 min centered near the period of interest are shown in Fig. 4. The winds are 9 m s⁻¹ from the northeast through the entire boundary layer with only slight shear at the inversion.

5. Mean cloud structure

The 3.2-mm and 32.8-cm wavelength radar observations are combined to examine the mean structure of the two cumuli as they pass over the site. Each radar provides a focus on specific elements of nonprecipitating shallow cumuli, and in the case of the profiler, the nearby environment. The large ratio between radar wavelengths and droplet size in nonprecipitating shallow cumulus ensures that the wind profiler is detecting mainly irregularities of the index of refraction and the cloud radar is detecting only Rayleigh scattering from cloud droplets. The Bragg scattering from the profiler can be used to study cloud entrainment and mixing. In addition to the differences in the two types of scattering detected by these radars, the cloud radar has much higher spatial and temporal resolution than the wind profiler. These differences in the radar sampling and scattering mechanism provide important contrasts of the two-dimensional images of the penetrating cumulus sampled by these systems.

The 94-GHz reflectivity and the 915-MHz profiler SNRs from 0850 and 0930 LST as the two cumuli of interest pass over the site are shown in Figs. 5–7. A threshold of −6 dB was applied to the profiler SNR values shown in Fig. 5. The LCL calculated from the 15-m temperature and humidity was about 800 m at this time. The inversion before and after the two clouds move overhead is well defined at 1600–1700 m by a narrow region of high wind profiler SNR values. From the inversion to about 1 km there is a layer of very low SNRs surrounding the two clouds. The maximum values of SNR at the inversion are located where the shallow cumuli penetrate the inversion interface. Bragg scattering minima are observed in the interior of the cloud, which is consistent with more homogeneity in the cloud core than at its edges. There are also relative minima in the profiler SNRs below each of the two clouds that indicate relatively homogeneous humidity conditions in the subcloud area feeding these clouds. Similar minima are observed below other clouds that moved over the profiler during the 14 h of observations shown in Fig. 2. We will show later, that the regions in the cloud layer where minimum wind profiler reflectivity is observed correspond to strong, unmixed updrafts observed by the cloud radar. The penetration of strong SNR values into the inversion layer is about 150 m and is a result of strong updrafts impinging upon the inversion layer.

The 94-GHz cloud radar reflectivity mappings of the two cumuli are shown in Figs. 6 and 7. The downwind side of these clouds and the cloud-top area are regions of high reflectivities, reaching values of −18 dBZ. The cloud boundaries are defined by reflectivities as low as −31 dBZ. There is evidence of detrained cloud matter at the inversion associated with a relatively flat cloud top extending upwind. The cloud top observed before the main core reaches the observing site is about 150 m below that associated with the core. Cloud base from the reflectivity is not sharply defined, although returns as low in altitude as 950 m (the LCL of near surface air) are observed in both cases. Since the mean horizontal wind speed in the cloud layer is about 9 m s⁻¹, the horizontal extent of the cloud is estimated to be about 1 km compared with a vertical extent of about 700 m.

The dynamics of these clouds can be investigated using the vertical velocities and spectral width calculated from the Doppler spectra. Figures 8 and 9 show the velocity field inside the two cumuli. Both, but particularly the first cumuli, have well-defined, vertically oriented updraft cores with maximum velocities of 5.5–6.0 m s⁻¹. The vertical gradient of vertical air motion (dw/dz) in the interior of the cloud is approximately 10⁻² s⁻¹ just below the inversion and reaches −2.5 × 10⁻² s⁻¹ above the base of the inversion. The updraft cores coincide with the areas of highest reflectivities observed in the cloud by the MCR. The strong updraft cores are associated with increase of the radar reflectivity with altitude, a combination that indicates the possibility of adiabatic-unmixed parcels. There is no evidence for penetrative downdrafts within the updraft core. There is, however, substantial vertical velocity variability within the detrained air observed upwind of the strong updraft.

The radar reflectivity intensities from the two radars show distinct differences (Fig. 10) that can be used to further examine the dynamics of the clouds. The wind profiler reflectivity obtained for the first cumuli (cloud A) is minimized in the interior of the cloud regions where the cloud radar reflectivity is high and the mean Doppler velocity indicates a strong updraft. These weak Bragg echoes in updraft regions are consistent with a nearly laminar flow in the updraft interior as suggested by Knight and Miller (1998). The steadiness of the updraft flow is further supported by consecutive profiles of Doppler velocity that show horizontal homogeneity of the vertical velocity in the updraft and gradual acceleration with height. If the updraft core is associated with small water vapor variability, then we expect the Bragg air turbulence scattering to be weak. Furthermore, at the cloud top the reflectivity from the MCR returns coincides with high reflectivity from the wind profiler. As expected, in the region where the updraft core penetrates the very dry air at the inversion layer a Bragg scattering maximum is observed. This scattering maximum may be induced by sharp humidity gradients across the interface between the saturated cloudy air and the unsaturated dry air at the inversion. Another possible mechanism is the entrainment of dry air into the cloud that causes inhomogeneities with scales close to λ/2 (≈16 cm) of the profiler. The MCR Doppler velocities observed at the cloud top, which showed downward moving parcels originating from the cloud top along the lateral boundaries, supports this possibility. The profiler Bragg scattering returns appear to be enhanced at the lateral cloud boundaries due to large moisture gradients. These echoes extend beyond the cloud boundaries defined by Rayleigh scattering observed with the cloud radar, which suggests that moisture gradients may be enhanced away from the boundaries by the humidity halo effects described by Perry and Hobbs (1996).

Two types of downdraft structures are identified in both cumuli sampled. One originates from near cloud top on the approaching (downwind) side of the cloud. The other penetrates through the cloudy air that detrains on the retreating (upwind) upper boundary of the cloud. The nature and the cause of these downdrafts will be further discussed in the next section, but we note here that, in the downdraft along the downwind cloud edge, the radar reflectivities are low, indicating that mixing may deplete the liquid water content. Inside the penetrative downdrafts in the trailing detrainment area, the reflectivities are relatively high. An inspection of the MCR Doppler spectra collected in this area indicates that the higher reflectivities here may be due to the presence of some larger drops in the radar sampling volume.

The Doppler spectrum width obtained in cloud A (Fig. 11) is used to further examine mixing and microphysical processes in this cloud. The interpretation of the spectral widths, which was discussed above, is difficult in general since several physical processes can produce Doppler broadening. Since the MCR has a relatively small sampling volume and high temporal resolution, comparison among the spectral width and the first two Doppler moments provides a basis for interpreting the spectral widths. The lowest spectral widths of 0.2–0.4 m s⁻¹ are observed in the updraft interior. This is a strong indication of less turbulent flow associated with relatively weak horizontal variability of vertical air motions and a gradual accelerating motion in the vertical. However, at the edges of the updraft, the spectral width increases substantially to about 1.0–1.2 m s⁻¹, especially in the narrow areas between the updrafts and downdrafts. The highest spectral widths are observed along the edges of the penetrative downdraft in the trailing detrained cloud area. The causes for this broadening will be further investigated in the next section.

6. Cloud processes

a. Updraft–downdraft circulations

In the previous section it was demonstrated that the cloud structure is characterized by coherent updraft and downdraft structures. Figure 12 shows a horizontal section of the Doppler spectrum moments through the first cloud at a height of 1700 m. In the description, the terms “upwind” and “downwind” are used to describe locations relative to the cloud core. We intentionally avoided the use of “up-shear” and “down-shear” since the wind profiler observations show no vertical shear. The use of “upwind” and “downwind” is made with no inference about processes. At the upwind side of the cloud the negative velocities are well correlated with low reflectivities that may result from the evaporation of cloud droplets as air descends in the downdraft along the edge of the cloud. In the cloud interior, the penetrative downdraft is associated with high cloud radar reflectivities. The sharp horizontal gradients of vertical velocity overlap with local maxima of the spectrum width due to wind shear effects on the Doppler spectrum. The vertical velocity variation across this cloud at 1700 m is strikingly similar to the aircraft observations from previous studies (e.g., Fig. 7, Warner 1977) that shows downdrafts at both side of the updraft. The narrow spectra width and its association with higher reflectivites in the cloud updraft is clearly illustrated. Small-scale variability in w, dBZ, and σ_w are greatest in the upwind side of the cloud.

To illustrate the nature and the cause of the downdraft characteristics, we consider representative examples of Doppler spectra from three different areas of cumulus cloud A as identified in Fig. 8. Within the updraft (Fig. 13a), the spectrum is relatively narrow and symmetrical—features consistent with broadening by turbulence only. A broader and skewed spectrum (Fig. 13b) is observed in the downdraft area on the upwind side of the cloud. The skewness of the spectrum at higher fall velocities and the relatively high reflectivity observed in this region are consistent with the presence of larger droplets. Although there is also broadening of the Doppler spectrum in the downdraft observed on the downwind boundary of the cloud (Fig. 13c), the Gaussian shape of the spectrum in this region is consistent with broadening due to turbulence and shear rather than the presence of larger droplets (Babb et al. 1999). The relatively low reflectivity in this region further indicates the lack of large droplets.

A more detailed depiction of the main updraft and downdraft regions of the cloud is shown in Figs. 14 and 15. In Fig. 14, the focus is on the downdraft observed on the downwind edge of the cloud. The mixing of the environmental air above the inversion at cloud top with cloudy air may cause this downdraft. The mixture becomes negatively buoyant, but still contains cloud droplets that can be detected by the cloud radar. The downdraft extends to near the base of the cloud and has a lateral extent of 100 m or less. The maximum downward velocity is about −3.5 m s⁻¹. Low reflectivity and narrow nonskewed Doppler spectra are consistent with the lack of large drops at the lateral downdraft (Fig. 14). Therefore the observed negative velocities appear to be associated with buoyancy driven downdrafts and cannot be attributed to the fall velocities of larger droplets that would tend to enhance the reflectivities and produce nonsymmetrical spectrum.

In the penetrative downdraft observed near the cloud top on the upwind side of the updraft, the relative high reflectivities complicate the interpretation (Fig. 15). The penetration depth of the downdraft is 200–300 m with a horizontal extent of about 150 m. The observed velocities do not exceed −2 m s⁻¹. At the downdraft boundaries, the broadening of the spectra may be due to sharp horizontal gradients in the vertical wind (Fig. 15) or turbulence generated by this shear. But in the broader downdraft area near the flat part of the cloud top the Doppler spectra are skewed and have tails that are consistent with the presence of larger droplets.

In the updraft, high reflectivities and upward velocities are associated with narrow spectra; this is consistent with cloud droplet distributions generated through adiabatic ascent. The undiluted nature of the updraft core is further supported by the vertical profile of adiabatic values of dBZ. Figure 16 shows a profile of reflectivity observed inside the updraft core compared with adiabatic values of dBZ calculated by assuming a monodispersed drop size distribution and a constant concentration. The adiabatic values of liquid water content (LWC) were calculated using the Miami sounding and the surface temperature and moisture values from the RSMAS site. The adiabatic reflectivity profiles were then calculated for assumed droplet concentrations of 100, 150, and 200 cm⁻³. Up to about 500 m above cloud base the reflectivities indicate cores that are close to adiabatic. The presence of unmixed adiabatic cores is further supported by the magnitude of the updraft below the inversion that is close to 5.5 m s⁻¹. This is very close to the magnitude of updraft estimated using a simple adiabatic cloud parcel model applied to the Miami soundings. Convective available potential energy (CAPE) estimates using the soundings correspond to an updraft velocity of ≈6 m s⁻¹ at 1600 m. Above 1600 m the effects of the inversion on both the reflectivity and velocity are apparent. Although the vertical velocity peaks at about 1600 m as the cloud core experiences the inversion, the reflectivity continues to increase to a maximum at about 1750 m (Fig. 17). The reflectivities above the inversion departs significantly from the initial near adiabatic values. The spectrum width remains constant up to the cloud top, indicating that the deceleration of the cloud core is gradual; no large-drop tail is observed in the Doppler spectrum. A nonentraining parcel moving upward at 6 m s⁻¹ into a layer where potential temperature is increasing at about 30°–40°C km⁻¹ (approximately the rate of increase for the Miami soundings) would penetrate about 170–200 m, a distance similar to that observed. At the trailing part of the cumulus cloud we observe upward and downward moving parcels with smaller horizontal and vertical scales and moderate velocities. In this part of the cumulus clouds it is possible that water contents will be less than adiabatic and more variable in the horizontal. This region of higher variability may correspond more closely to observations that have been made with aircraft in some studies.

The Miami soundings were used to determine if environmental conditions could support downdrafts generated by mixing of cloud air and air from above the capping inversion. The temperature and moisture jumps across the inversion were used to estimate the jumps in total water q_t and equivalent potential temperature θ_e. Since the adiabatic cores appear to reach the inversion, the total water jump was estimated from the value of the mixing ratio in the subcloud layer and the mixing ratio above the inversion. The estimated values are Δq_t ≈ −8 g kg⁻¹ and Δθ_e = −15 K. In this case, the criterion for cloud-top entrainment Instability (Kuo and Schubert 1988),

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is satisfied for a wide range of κ values ranging from 0.23 (typical) up to 0.7 (including mixing processes). Thus air from above the inversion that mixes with the cloudy air at the top of the core can result in mixtures that are negatively buoyant relative to the cloudy air.

b. Turbulence and wind shear

Doppler spectra observations of precipitating systems made previously with centimeter radar were used to detect and estimate turbulence and wind shear. (Lee 1977; Knupp and Cotton 1982; Istok and Doviak 1986). These observations were useful in characterizing the turbulence and wind shear in severe storms.

Information on wind shear and turbulence in the radar resolution volume can be retrieved from the Doppler spectrum moments. Similar retrievals can be made using the MCR observations of fair-weather cumuli at vertical incidence. The lack of broad Doppler spectra in the area where the active cloud core penetrates the inversion and the presence of broad spectra at the interfaces between updrafts and downdrafts supports the idea that shallow cumuli are comprised of a large population of cloud parcel ensembles. Since the narrow beam of the cloud radar (about 6.5 m at 1.5 km) samples a fixed volume for 1 s as convective elements are advected through the beam at a speed of 8–9 m s⁻¹, wind shear can induce bimodal or multimodal Doppler spectra shown in Fig. 18. The velocity separation between the peaks of this bimodal spectrum cannot be explained by a realistic drop size distribution. Furthermore, this spectrum was obtained in a region where the reflectivities are relatively weak. The presence of these spectra can be explained only by the occurrence of sharp horizontal gradients in the vertical velocity. Most of the double peak spectra are due to vertical air motion horizontal gradients. Inside the updraft core we observe the strongest vertical velocity shear with height, k_υ ≈ 10⁻² s⁻¹ and k_h = 10⁻¹ s⁻¹. The high values of vertical velocity shear across the horizontal dimension are confined to the vertical interfaces between the updraft and the downdraft. The k_h values in the interior of the updraft core are much lower. This is related to vertical velocity continuity in the vertical, even where the cloud interacts with the environmental inversion. The vertical gradient is weak and even though the larger dimension of the radar sampling volume is in the vertical, there are no double peaks inside the updraft. Furthermore, the vertical air motion changes linearly throughout the beam so that shear cannot produce bimodal spectra (Doviak and Zrnic 1993). But the transition in the horizontal dimension from an upward moving parcel to a downward moving parcel is very sharp and can occur within the very narrow horizontal dimension of the radar beam (6.5 m) and during the short sampling period (1 s) as the cloud advects through the radar sampling volume. The capability of the cloud radar to provide high velocity and sampling resolution allows for a detailed mapping of the cloud structure and a separation of detailed velocity differences. Most of the double-peaked spectra observed have two distinct Doppler peaks, indicating that the transition zone was narrow. Such horizontal discontinuities in the vertical air motion support the idea of no mixing of downdraft air into the updraft.

As discussed above, the narrowest Doppler spectra are in the interior of the unmixed core. These spectra are almost perfectly Gaussian, with small Doppler spectrum width values, which implies a narrow drop size distribution. These narrow spectra, unaffected by wind shear or droplet size distribution broadening, can be used to estimate eddy dissipation rates ε. Consequently, it is reasonable to assume that the observed Doppler spectrum width in the unmixed updraft is mainly due to turbulence broadening (σ² ≈ σ²_t).

Figure 13a shows a representative Doppler spectrum observed in the updraft regime. The spectrum is almost Gaussian with no apparent skewness due to the drop size distribution. Under the above assumptions and following the previous discussion of Doppler moments, second moments of the Doppler spectrum can be used to estimate the turbulence dissipation rate ε (Frisch and Strauch 1976; Istok and Doviak 1986). Here we estimate ε only in the unmixed updraft core—an area of the cloud that most closely satisfies the assumptions about drop size distribution and wind shear broadening. The same method could be applied to the entire cloud if the wind shear effects could be removed.

Figure 19 shows the calculated eddy dissipation rates within the updraft core. Typical values inside the updraft core are 10–40 cm² s⁻³. Near the boundaries of the updraft core, however, the assumptions weaken and the retrieval is subject to errors, mainly due to contribution from the wind shear broadening. The retrieved values of ε are very useful for the determination of timescales such as that for turbulent mixing τ_m, and droplet evaporation τ_d (Baker et al. 1984; Jensen et al. 1985). The timescale for the decay of turbulence is given by

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For an eddy scale of 200 m, τ_m is approximately 3–4 min for typical values of dissipation rates inside the updraft.

7. Conclusions

This study uses observations from a short-wavelength radar to define the in-cloud vertical structure of classic marine fair-weather cumuli. By doing so we add a missing component of aircraft measurements of these clouds—vertical definition of updraft and downdraft structures. Doppler spectra obtained from the radar in two shallow cumuli provide mean vertical velocities as well as detailed spectral shapes that can be used to infer small-scale vertical velocity shear, illuminate cloud microphysical processes, and estimate turbulence dissipation rates. These new observations facilitate the analysis and understanding of in-cloud circulations and the physical processes involved, since the cloud boundaries and dimensions are mapped along with the internal structure of the clouds. Observations from a longer wavelength radar (wind profiler) were used to provide further definition of the turbulence structure in the cloud and the environment of the clouds.

The high temporal and spatial mapping of the in-cloud structure revealed coherent vertical structures. The observations document for the first time detailed vertical and horizontal dimensions of updraft and downdraft circulations in fair-weather cumuli. The two cumuli studied in detail have similar circulation patterns—an updraft core surrounded by downdrafts. Maximum updraft velocities are about 5.5 m s⁻¹ in clouds with vertical extents of about 700 m. The existence of adiabatic cloud cores is supported by vertical velocities and reflectivities values close to those produced by simple adiabatic cloud parcel model. These findings support the conclusions made by Knight and Miller (1998) using observations from longer wavelength radars. The updrafts remain unmixed as they penetrate about 150 m into the capping inversion layer where detrainment is evident by a relatively flat cloud top extending upwind. The vertical extent of the updrafts is 400 m and the horizontal extent is only 250–300 m. Minima in the the 94-GHz Doppler spectra and the 915-MHz Bragg scattering returns indicate that turbulent fluctuations in the updraft are minimal compared with other parts of the cloud. Maxima in the Bragg returns are observed in the regions where the updrafts penetrate the capping inversion and along the lateral boundaries of the cloud.

The observations clearly indicate the presence of downward moving parcels that originate from the cloud top. At the downwind side, mixing results in negatively buoyant parcels that extend downward to cloud base. At the upwind side there is evidence of downdrafts penetrating through detraining, dynamically inactive parts of the cloud matter. These downdrafts have horizontal dimensions of about 150 m, penetrate about 200 m into the cloud, and have maximum vertical velocities of about 200 m. Detailed analysis of the Doppler spectrum width at the in-cloud boundaries between up- and downdrafts revealed the existence of sharp discontinuities of the vertical velocity in the horizontal. Furthermore, the updraft core in one of the clouds analyzed has a structure that is consistent with the idea that cumulus clouds comprise several successive bubbles that emerge from the subcloud layer. It is clear that even small cumuli should be considered as a convective complex rather than a simple active growing element that later decays into a passive cloud mass. The same may not be true of continental clouds that are forced from below by strong thermals.

The observations provided in this manuscript help put many previous aircraft observations in perspective. Vertical velocities obtained as a function of time at a fixed height through the core of the cloud indicate a spatial structure that is strikingly similar to those obtained from some aircraft penetrations (Warner 1977) with downdrafts on both sides of the updraft. Regions of higher vertical velocity variability observed with the radar were observed in the detraining air masses of the clouds. This also appears to be a region in the cloud where entrainment processes are most active. Aircraft observations that indicate high vertical velocity variability may well be made in areas of the cloud that are easily defined visibly, but represent cloud matter in a latter cycle of the cloud evolution. Warner (1977) discusses the difficulties in determining which part of the life cycle of a cloud is being sampled during aircraft penetrations. The results shown here indicate that the active updraft region occupies a relatively small part of the cloud. Thus even penetrating the adiabatic core of an active cumulus complex may not be assured by flying through the visible cloud.

This study illustrates the maximum potential of cloud radars. Fair-weather cumuli are very difficult meteorological targets to observe. Their small volume and their composition of relatively small droplets limit the use of longer-wavelength radars. Since the lifetime of the clouds is small it is difficult to make aircraft penetrations at multiple levels. In addition to providing reflectivities and mean Doppler motions in the clouds, millimeter-wavelength radars can provide full Doppler spectra that can be used to obtain critical information on physical processes and their interaction with updraft and downdraft structures. Furthermore, the radar has great potential for studying the early precipitation stages of deeper cumulus clouds and, when used on a mobile platform, for studying the structure of fair-weather cumuli through their entire life cycle. When used in a scanning mode, the radar has the potential for providing more on the three-dimensional structure of the clouds. Currently, however, the retrievals from the radar cannot provide the microphysical detail that is available from in situ aircraft observations. As the retrieval techniques for cloud radar become more sophisticated, it will be possible to further advance our understanding by providing critical observations for process studies and the direct evaluation of cloud models. The improved understanding of the cloud dynamics and microphysics will be critical in the development of parameterizations for larger-scale models.