1. Introduction
The formation of precipitation in warm clouds involves three steps: activation of cloud condensation nuclei (CCN), mainly at the cloud base; condensational growth of the activated nuclei as cloud droplets; and finally formation of precipitating drops via collision and coalescence between droplets and drops. This last mechanism becomes efficient as soon as a few droplets bigger than 40 μm in diameter have been formed.
The onset of precipitation in convective clouds remains however a puzzle for cloud microphysicists. The efficiency of this process calculated with detailed microphysical models seems to be too small to account for the initiation of precipitation by the collision-coalescence process (Pruppacher and Klett 1978, p. 430). Two circumstances have contributed to focus the attention of the cloud physics community on this subject: on the one hand, numerical simulations of the collision–coalescence process have shown that the production of droplets with diameters larger than about 40 μm is a crucial step for precipitation formation (Bartlett 1970);on the other hand, in situ measurements in convective clouds have revealed that actual droplet spectra are much broader than spectra predicted by the current theory of condensational growth (Warner 1969a,b). The classical theory implies that the droplet growth rate is inversely proportional to the droplet size, so that small droplets are growing faster (in diameter) than the big ones. After the initial spectrum has been formed by CCN activation, it evolves toward larger sizes and becomes narrower. In an adiabatic rising cloud cell (see section 2), the rate of condensation is then too slow for the biggest droplets to grow to a diameter of 40 μm before reaching the top of shallow cumulus clouds. Since then, various attempts have been made to identify additional processes acting in real clouds that would explain the deficiency of the numerical simulations. The proposed explanations can be ranged into three classes: (i) precipitation embryos, such as ultragiant nuclei, preexist to the cloud; (ii) the efficiency of the collision-coalescence process is underestimated by the models; or (iii) there are cloud processes, in addition to the classical water vapor diffusion process, that are acting for broadening the droplet spectra. It is however important to recognize that the basis of spectra broadening, namely, the observation of broad spectra in cumulus clouds, is questionable. Clouds are heterogeneous and droplet sampling over long heterogeneous regions always produces broad spectra, while locally they can be very narrow. Because collision efficiency is determined by the local properties of droplet spectra at the microscale, sampling artifacts can lead to erroneous interpretations. In addition, airborne spectrometers also broaden artificially the actual spectra. It is thus relevant to reconsider the basis of this process each time measurements are improved. This series of papers makes use of recent droplet spectra measurements with a new airborne spectrometer to examine spectra-broadening processes.
a. Ultragiant nuclei
The condensational droplet growth theory in an adiabatic cell is unable to generate a broad spectrum made of medium size droplets (e.g., 10 μm in diameter) and big droplets as big as 40 μm in diameter, if such big particles do not already exist at the cloud base. In fact the theory [Eq. (1) in section 2] implies that the rate of growth of the droplet surface is the same for all the droplets in a uniform field of supersaturation. It follows that 40-μm diameter droplets can coexist with smaller droplets (10 μm) only if their initial diameter ϕi at the cloud base was already of the order of
Such particles have been documented by Woodcock (1953) over the ocean and their impact on precipitation formation has been analyzed by Johnson (1982). These rare particles are difficult to observe in situ, but there are a few signs of their presence around clouds. For example Laird et al. (2000) have built composite spectra of the particles measured outside clouds during the Small Cumulus Microphysics Study (SCMS). By integration of the measurements over large distances they reveal, with a significant confidence level, concentrations of large particles (50 and 100 μm in diameter) of 0.225 and 0.002 L−1, respectively. They conclude that these UGNs are a viable explanation for the onset of precipitation in SCMS clouds.
The general picture suggested by recent studies is a large consensus between various numerical approaches to confirm that UGNs could be efficient precipitation embryos as long as their diameter is greater than 40 μm and their concentration of the order of a few tens per m3. Their origin is not clear, either large CCN, or mineral dust coated with sulfate (Levin et al. 1998), or insoluble particles acting as coalescence embryos (Lasher-Trapp et al. 1998). It is still a challenge to demonstrate experimentally the presence of such particles during the initial stage of cloud development. Existing particle counters are not well suited because their sampling section is far too small for measuring such low concentrations with a high confidence level. However, one can also consider the significant values of Rayleigh reflectivity measured with ground radars at the early stage of cumulus development as a corroboration of the existence of UGNs.
b. Collision–coalescence efficiency
Since the onset of precipitation is directly related to the ability of condensation droplets to coalesce and form the initial precipitation embryos, there is a possibility that present calculations underestimate the actual probability of collision and coalescence of the small condensation droplets. Efforts in this field have been so numerous that a significant confidence can be attributed to the existing schemes. However, a new concept has been recently introduced by Pinsky and Khain (1997) and Khain and Pinsky (1997). It is based on droplet inertia-induced effects. During their centrifugal motion outside of the turbulent vortices, droplets of similar sizes can experience colliding trajectories. Collision is an instantaneous process, and only a very few inertia-induced colliding trajectories could be sufficient to enhance significantly the probability of collision of small droplets. This recent concept is thus a promising way to explore for a better understanding of the onset of precipitation.
c. Droplet spectra broadening
The broadening of the droplet spectra in cumulus clouds is a phenomenon that has been largely discussed in the literature since in situ observations by Squires and Warner in the sixties. The observations show broad droplet spectra while the idealized model of droplet growth in an adiabatic convective cell predicts narrow spectra. The width of the droplet spectrum is a crucial parameter for the calculations of collision-coalescence between droplets. The liquid water content (LWC), the mean volume diameter of the droplet size distribution and the proportion of big droplets are also key factors. The question is thus not limited to the observation of broadening, which refers only to the width of the droplet spectrum. In the comparison between an observed spectrum and the adiabatic reference, the relative droplet concentration in each size category shall be considered. Of major impact is the presence of big droplets in proportion larger than in the adiabatic reference, which will be referred to here as superadiabatic droplet growth.
This series of papers is dedicated to the experimental study of droplet spectra broadening (DSB) in cumulus clouds. Our main concern is to differentiate between various potential sources of broadening and superadiabatic droplet growth, which have been proposed in the literature in order to design an experimental methodology for the evaluation of their respective contributions to the onset of precipitation. The β2 scheme used here for the calculation of droplet condensational growth from an initial spectrum at the cloud base is presented in section 2. In section 3, the dataset is briefly described, and the procedure for the selection of the initial spectra is presented. Finally various concepts proposed to explain DSB are discussed, our experimental methodology is presented, and the contribution of each paper in the series is summarized. Section 4 is dedicated to the assessment of the accuracy of droplet measurements made with the Fast-Forward Scattering Spectrometer Probe (FSSP) and to the estimation of the instrumental contribution to the observed DSB. The observations are analyzed in section 5 and the results are discussed in section 6, followed by the conclusion in section 7.
2. The β2 scheme
a. Reference adiabatic model for droplet growth
The β2 scheme has been already used in Brenguier (1991) and in Brenguier and Grabowski (1993). It is important to note that this formulation is much more efficient than the conventional integration of droplet growth with a binned distribution. In this later case, errors in the evaluation of the supersaturation and numerical diffusion are accumulated during integration and the droplet spectra are numerically broadened. On the opposite (2) and (3) provide an analytical solution, formally equivalent to the complete integration of a binned distribution, as long as the equilibrium supersaturation Se can be neglected. Examples of use will be presented in this series for the calculation of adiabatic growth in Part I, for the effects of small-scale fluctuations of the supersaturation in Chaumat and Brenguier (2001, hereafter Part II), and for the effects of entrainment-mixing processes in Part III (manuscript in preparation).
Figure 1 illustrates the two representations (ϕ and ϕ2 distributions). The initial spectrum is shown on the left. The size distribution in Fig. 1a gets narrower with condensational growth according to Eq. (1). Three spectra are represented with the same LWR but different droplet concentrations, C, C + 50, and C − 50 cm−3 in order to show the effects of the variability of this parameter. The change in the spectral shape prevents direct evaluation of DSB. Figure 1b shows the same calculations with the surface distribution. The curve labeled (C) corresponds to the initial spectrum shown on the left and it has been simply obtained by a translation along the ϕ2 axis. In this example C = 225 cm−3 and ΔqA(z0, z) = 3.31 g kg−1. The uncertainty range of ±50 cm−3 for the droplet concentration is typical of the uncertainty in the measurements of droplet size distributions at such a value of droplet concentration. Part of this uncertainty scales with the droplet concentration but not proportionally (Brenguier et al. 1994). For simplicity the uncertainty range considered here is set at ±50 cm−3, irrespective of the value of droplet concentration. The effects of macroscale fluctuations of the droplet concentration will be further examined in Part III.
b. DSB and deviations from the reference model
Various physical processes can be interpreted in terms of Ψ(β2, z).
1) Microscale fluctuations of the supersaturation
One can imagine the case of an adiabatic convective cell, with a mean droplet concentration C. If the supersaturation field is not uniform, the droplets are experiencing different values of supersaturation and the Ψ(β2, z) function is no longer reduced to a Dirac at the value
2) Mixing
One can also imagine that the observed spectrum is the result of the mixing of droplets having followed different trajectories. The Ψ(β2, z) function can be reconstructed if the β2 value and the probability of occurrence of each trajectory can be calculated. This type of formulation has been used in Brenguier and Grabowski (1993) for the numerical simulation of the effects of turbulent mixing on droplet spectra, in an Eulerian frame. In this case, it was assumed that the activation process produces the same initial spectrum, everywhere activation is occurring, so that the droplet concentration is the same for all trajectories. If this condition is removed, the scheme can however be extended by providing the probability density function (PDF) of initial spectra.
In conclusion, the β2 scheme is efficient for analyzing various processes potentially responsible for DSB. The only exception is for processes based on size dependence of the growth equation. The authors are presently not aware of any such physical process potentially able to reinforce the growth of the largest particles.
3. The data and the methodology
a. The SCMS dataset
The data presented in this series have been collected in 1995 during the SCMS experiment at Cocoa Beach, Florida. Nonprecipitating shallow cumuli (diameter of the order of 2 km and depth smaller than 3 km) growing along the coast of Florida (Cape Canaveral) were observed with a ground radar and sampled with three coordinated aircraft: the NCAR C130, the University of Wyoming King-Air, and the Météo-France Merlin-IV. The analysis is based on data collected during the 10 flights performed by the Merlin-IV between 4 and 12 August. The droplet spectra were measured onboard the Merlin-IV with the Fast-FSSP. This instrument, described in detail in Brenguier et al. (1998), is an improved version of the FSSP-100.1 For each flight, Fast-FSSP measurements performed at the cloud base were analyzed for the selection of the initial spectrum. Then, measurements performed at higher altitudes were examined to determine how observed spectra compare to the adiabatic reference.
b. Selection of the initial spectrum
The characterization of the initial spectrum requires the definition of the cloud-base altitude, pressure, and temperature. This initial spectrum can be calculated with an activation model if the vertical velocity at cloud base and the nucleation properties of the CCN are known. The initial spectrum can also be directly measured slightly above cloud base.
Fluctuations of the vertical velocity at the cloud base result in a significant variety of initial spectra. Broadening of an observed spectrum can thus be assessed only if the shape of that spectrum (ϕ2 distribution) is much broader than the shapes of all the initial spectra observed at the cloud base. The total number concentration of activated nuclei at the cloud base, C, is an important parameter. At a fixed value of cloud-base temperature and pressure, the adiabatic calculation provides a unique value of liquid water mixing ratio, qA(z), at an altitude z above cloud base, irrespective of the value of droplet concentration. Therefore the mean droplet volume in an adiabatic spectrum,
In this series of papers, observed spectra are compared to adiabatic calculations to evaluate DSB. In this case, the initial spectrum has been derived from measurements made slightly above cloud base. As the same aircraft was used for both levels, it was not possible to measure the initial spectrum of a cloud cell, which was further sampled higher in the cloud. In fact both series of measurements were separated in time by up to 1 h. However, the spectra measured at cloud base on a given day show similar shapes, mainly determined by the CCN properties, with a range of droplet concentrations similar to the values measured higher in the cloud. Our methodology for the definition of the initial spectrum thus consists in the selection of spectra measured slightly above cloud base, in regions of updraft to define f0(ϕ2, z0) (total concentration C0). The spectra measured at cloud base have also been compared to spectra calculated with a detailed activation model initialized with the nucleation properties of CCN measured in situ onboard the NCAR C-130 in the boundary layer. The calculated spectra are always narrower than our selection of initial spectra. Our method thus slightly underestimates DSB compared to an estimation based on an initial spectrum derived from activation calculations. Therefore, we are not considering here processes that could broaden the initial spectrum during the activation phase, but only broadening processes acting from slightly above the activation level to the upper levels in a convective cloud.
The scaling procedure allows one to compare the observed spectrum with an adiabatic spectrum containing the same specific concentration of droplets.
Natural variability of the total droplet concentration at cloud base and of the shape of the initial spectra thus limits the sensitivity of the experimental method for the detection of DSB. Nevertheless, it must be noticed that the spectra observed higher in the cloud, even the narrowest ones, are always broader than all the spectra observed at cloud base in regions of updraft. The observed DSB cannot thus been attributed only to uncertainties in the selection of the initial spectrum.
c. Concepts and methodology
Natural variations of the total droplet concentration are a potential source of DSB. The processes contributing to the variability of the droplet concentration are the fluctuations of the vertical velocity at cloud base and the entrainment-mixing processes. Mixing of cloudy air with the environmental dry air results in a dilution of the droplet concentration. In addition some droplets are evaporated to compensate the deficit of water vapor in the entrained air. Depending on the proportion of entrained air and its water vapor deficit, all rates of dilution are possible down to 100%, that is, all the droplets can be completely evaporated. Low values of droplet concentration have however a short lifetime in ascending cells because the supersaturation is rapidly increasing and additional CCN are activated. Droplet evaporation by mixing and the secondary activation process are reflected in the droplet spectra observed higher than the cloud base by significant proportions of small droplets. The basics of DSB due to the variability of droplet concentration is simple but its experimental description is not trivial (Telford et al. 1984). If cloud entities with various values of droplet concentration had a long lifetime, it should be likely to sample such entities with an instrumented aircraft and to observe an anticorrelation between droplet concentration and droplet sizes. Such observations have not been reported except close to the cloud base, where they mainly reflect the variability of the vertical velocity at the activation level. The fact that the phenomenon is not currently observed in airborne measurements suggests that it proceeds by short steps whose cumulative effects could contribute to DSB, while each step is not detectable separately. In addition to their effects on concentration fluctuations, entrainment-mixing processes are potentially able to broaden the droplet spectra, at constant droplet concentration. If only part of the droplet population is evaporated during the mixing with dry air, the remaining part being unaffected (Baker and Latham 1979), the resulting spectrum is made of unchanged and partially evaporated droplets and it is broader than the initial spectrum. Secondary activation of CCN in a convective cell also generates DSB. More generally, mixing of parcels following different trajectories in a cloud and experiencing various levels of condensational growth or evaporation always lead to some DSB. In some circumstances, a broad spectrum made of droplets ascending adiabatically from the cloud base mixed with smaller droplets, either partially evaporated or resulting from secondary activation, is capable of enhanced condensational growth resulting in superadiabatic droplet growth. These various cases will be documented experimentally and simulated in Part III of this series.
The processes discussed above involve mixing of cloud cells with either different values of droplet concentration or different trajectories and condensational growth. They can be referred to as macroscale processes. In their simulation it is still however assumed that the condensation theory is valid, or more precisely that the supersaturation is uniform at the microscale. Manton (1979), Srivastava (1989), and Cooper (1989) have questioned such an assumption by considering microscale fluctuations of the supersaturation. The sources of variability are the randomness in the spatial distribution of the droplets and the turbulent fluctuations of temperature, humidity, and vertical velocity in the updraft. In these studies, only the variance of β2, the integral of S/w, was derived. Higher moments of the β2 distribution are difficult to predict with statistical models. Three-dimensional models of particles in a turbulent field are now used at the microscale for predicting the statistics of the integral of S/w, that is, the Ψ(β2, z) function along an adiabatic ascent. The possible contribution of the droplet spatial distribution to DSB will be explored experimentally in Part II of this series.
The distinction between macro- and microscale processes is not trivial experimentally, because there is no clear separation in the spatial scales of turbulence. Our approach in this series is rather based on the differentiation between two concepts for generating concentration heterogeneities: evaporation following mixing with dry air and droplet inertial coupling with turbulence. Mixing processes involve fluctuations of supersaturation associated with the entrainement of dry air from the environment. They act down to the Kolmogorov microscale but they do not involve coupling between droplet inertia and turbulence. In contrast inertial coupling and the resulting preferential concentration are associated to large centrifugal accelerations that are effective only at the microscale, but they do not involve fluctuations of the air properties. Our approach is thus based on the following assumption: if microscale inertial coupling processes had a significant contribution to DSB, it should not be possible to observe narrow spectra, in regions that are not affected by mixing processes, especially after more than a kilometer of convective lifting. Our objective in this first part of the series is thus to identify the narrowest spectra measured in the upper part of cumulus clouds sampled during SCMS and to characterize their DSB with respect to initial spectra measured slightly above cloud base and translated adiabatically by the value
Figure 2 shows time series of droplet number concentration, of the droplet spectrum, and of LWC (=ρaqa) along a cloud traverse. The droplet spectrum is represented by the 10% percentiles (dashed line), from 10% to 90%. The p percentile ϕp is the value of droplet diameter such that p% of the total number of droplets have a diameter smaller than ϕp. Superimposed with solid lines are the mean, the mean volume, and the effective diameters. Percentiles close to each other reflect a narrow spectrum. For example, in the subsection indicated by vertical bars in the figure, 80% of the droplets (from 10% to 90%) have a diameter between 23 and 30 μm. The procedure thus consists in the selection of cloud traverses showing subsections with narrow spectra, such as in Fig. 2. Droplet measurements are then cumulated over each subsection to build the mean ϕ2 distribution over that section. This procedure has been used to select 50 samples within the SCMS dataset.
Figure 3 shows an example of a narrow spectrum (solid line) in linear (top) and log (bottom) scales, measured at the altitude z = 2188 m. The dot-dashed line shows the initial spectrum, as it has been measured slightly above cloud base, at the altitude z0 = 715 m (left) and after a translation (right) of
4. Instrumental limitations
The characterization of narrow spectra with the current droplet spectrometer (FSSP-100) is difficult for three reasons: (i) droplet spectra are highly variable in clouds and regions of narrow spectra are short. A spectrum obtained by droplet counting over a long heterogeneous region is always broader than spectra observed at a smaller scale. Such a feature due to a sampling artifact has no meaning for the collision-coalescence process whose efficiency is only determined by the local properties of the spectra at the microscale; (ii) the size resolution of the instrument (3 μm in diameter) is of the same order of magnitude as the width of the reference spectrum; (iii) coincidences of droplets in the detection beam of the FSSP-100 broaden artificially the spectra toward larger sizes.
The measurements used here have been collected with the Fast-FSSP, a modified version of the FSSP-100 (Brenguier et al. 1998). New electronics provides information recorded for each detection, which includes: the amplitude of the detected pulse sampled on 255 size classes instead of 15 in the standard instrument, the pulse width and the interarrival time between detections with a resolution of 1/16 of μs, and information on the position of the droplet in the detection beam. Brenguier et al. (1998) describes how droplet spectra measurements have been improved with this instrument: (i) very fine spatial resolution can be obtained by using the optimal estimator (Pawlowska et al. 1997), which also provides information about the homogeneity of the sample. This resolution prevents sampling artifact due to spatial heterogeneity of the spectra. (ii) The size resolution is better than 0.5 μm over the whole diameter range. (iii) The third limitation relative to artificial broadening by coincidences is however identical for both instruments since the Fast-FSSP is based on the same optics as the standard instrument. Special attention has therefore been given to this possible instrumental artifact.
Cooper (1988) examined instrumental broadening of the droplet spectra due to coincidence effects with a probabilistic approach. The transfer matrix
Figure 4 shows three examples of narrow spectra observed in the upper regions of cumulus clouds, with three values of total droplet number concentration: 225 in (a), 329 in (b), and 455 cm−3 in (c). The observed spectrum is plotted with a dotted line and the reference adiabatic spectrum with a dashed line. The distributions are represented in linear (left) and log (right) scales. For the three examples, the concentration density peaks up to values between 1 and 10 cm−3 μm−2, at values of ϕ2 between 500 and 900 μm2. There is a significant difference between the observed and the reference spectra at large values of ϕ2, above 1000 μm2. The observed spectrum shows density values of the order of 0.01 cm−3 μm−2, while the reference spectrum rapidly drops below 0.001 cm−3 μm−2. Therefore, low probability coincidence events must also be considered.
The probabilistic approach of Cooper is no longer reliable at so small probability values (10−2–10−4). In fact the amplitude measured for a pulse of coincident droplets corresponds to the peak value of the detected pulse. This pulse is made of the sum of the pulses of the coincident droplets, so that its shape depends on the position of each droplet in the beam. For two particles the joint probability requires integration over all possible positions of the two droplets in the beam. For more than two particles, analytic integration is too inaccurate and the pulse shape must be calculated explicitly for all possible realizations. In order to evaluate precisely spectra broadening due to coincidences, Perrin et al. (1998) have thus developed a stochastic model. The actual spectrum to be tested is used to build a virtual random spatial field of a very large number of droplets in a volume swept by the instrument. The droplets are distributed randomly in space. The model of beam intensity and of the probe optics is then used to simulate the series of pulses generated by these droplets when they cross the probe’s sampling section.
The beam intensity profile has been measured in the laboratory and it is represented in the model cylindrical coordinates with a grid of 20-μm spacing along the beam axis, and 6.8-μm spacing along its radius. The sensitive part of the beam has a length of 2 cm and a constant radius of 110 μm over a length of 3 mm at the center, increasing up to 205 μm at the limits (±1 cm). The random droplet field is virtually moved through the beam with spatial steps of 6.8 μm. Each time a droplet is inside the sensitive beam volume, the scattered power is derived from the beam intensity at the droplet location and from the droplet diameter based on Mie scattering between 3° and 12°. The droplet image on both the signal and the slit detection diodes is calculated from the optical characteristics of the detection optics and the detected power is derived as the scattered power times the fraction of the image that is effectively collected by the diode active area. The scattered power is then cumulated over all the droplets simultaneously present in the beam. The detected power is converted to voltage according to the respective gains of the signal and slit amplifiers. The series of measured voltages form the simulated pulses that are compared to a threshold value to derive pulse duration, pulse amplitude, and the interarrival time between detections, as in the Fast-FSSP real-time processing module. The most convincing validation of the model is the remarkable similarity between the measured and simulated frequency distributions of pulse duration, for the total counts and depth-of-field counts [see Fig. 5 and 6 in Perrin et al. (1998)]. It can be noticed that the coincidence effects do not depend on the actual airspeed through the detection beam. Airspeed only matters when there is electronic attenuation of the pulses, at a speed larger than 150 m s−1 in the Fast-FSSP, while the aircraft was flying at 100 m s−1 at the most. Electronic noise is not considered in this simulation because its amplitude is between 10−2 and 10−3 of the nominal voltage for the droplet sizes considered here (between 20 and 30 μm in diameter). Electronic noise in fact affects droplet sizing only at diameters smaller than 5 μm.
The reference adiabatic spectrum is used to initialize the model of probe functionning and the simulated spectrum is represented in Fig. 4 by a solid line. The three examples show that spectra broadening by coincidences is significant even at values of droplet concentration as low as 225 cm−3, and that it increases with increasing droplet concentration. In particular, it shall be noticed that the plateau at about ϕ2 = 1000 μm2, which increases from density values of 0.01 cm−3 μm−2 at a concentration of 225 cm−3 to values of 0.1 cm−3 μm−2 at a concentration of 455 cm−3, is well reproduced by the simulation.
It is crucial to notice too that these effects of the coincidences affect both instruments, the Fast-FSSP as well as the FSSP-100. The differences between the two instruments, namely, the depth-of-field selection procedure (annulus vs slit) and the dead-time in the standard probe have a significant impact on the counted rate but the coincidence effects on spectral shape, that are mainly dependent upon the beam geometry, are similar. These effects have not been mentioned in previous studies of spectra broadening based on FSSP-100 measurements because the probabilistic approach of Cooper is limited to coincidences of two particules. Instrumental broadening does not explain the complete features of the observed spectrum, but it can be concluded from this test that the actual spectra sampled with FSSPs, either standard or Fast, are narrower than the measured ones. In particular, the presence of very large droplets cannot be accounted for as an actual phenomenon unless they can be tested by alternative measurements. However, the simulation shows that coincidence effects do not strongly affect the values of concentration density close to the mode of the distributions. In the three examples shown here and particularly in the first one, the observed spectrum is broader than both the reference spectrum and the one derived from simulation of coincidence effects. The measured spectrum in Fig. 4a shows superadiabatic values of concentration density from the mode of the spectrum (950 μm2) up to ϕ2 = 1400 μm2. Only this manifestation of superadiabatic droplet growth can be considered here as significant with regards to instrumental uncertainties.
5. Characterization of the narrow spectra
Each selected spectrum is then characterized by the Ψ(β2) function, which relates the observed spectrum to the initial spectrum. It is obtained by inversion of (4). The solid line in Fig. 5 is the Ψ(β2) function derived from the example shown in Fig. 3. The oscillations on the sides of the mode are not significant as they result only from the inversion technique. The value
Each Ψ function is then characterized by its mean value
There is still a significant uncertainty in this estimation because it is not possible to better estimate the instrumental contribution. The stochastic model of probe functioning is more accurate than a probabilistic model, especially for the effects of coincidences of more than two particles, but it cannot be inversed as the probabilistic model for correcting these effects in the measured spectra. It provides only an evaluation of instrumental broadening. This estimation of spectra broadening in adiabatic cores represents however significant progress with respect to the previous ones for two reasons: the better size resolution of the Fast-FSSP with respect to the standard probe and, for the first time, the estimation of multidroplets coincidence effects. Actual spectra in regions undergoing minimal mixing are possibly narrower, but the only rational conclusion at this point is that they are at least as narrow as indicated in Eq. (7). This relationship holds for the narrowest spectra observed in nonprecipitating cumulus clouds, within a range of droplet concentration between 100 and 1500 cm−3. Observations of such narrow spectra are documented up to altitudes of more than 1500 m above the cloud base.
6. Discussion
Our understanding of potential broadening processes in adiabatic cores is that droplets could be exposed to stochastic fluctuations of supersaturation along their trajectories and that the lifetime of the microscale supersaturation fluctuations should be short compared to the time needed for a particle to reach the observation level (150–300 s for the example shown in Fig. 3, at a vertical speed between 5 and 10 m s−1). Therefore the integral of S/w should be the sum of independent stochastic realizations of a random process. In such a case the central limit theorem implies that the values of the integral should be normally distributed, irrespective of the PDF of the local values of supersaturation. The tail of the Ψ(β2) function toward large values of β2 thus appears as a paradox, which could be resolved only if microscale turbulent structures had a lifetime comparable to the duration of the convective ascent. It is thus crucial to establish precisely the reality of these observations.
Simulations of the probe operation have demonstrated that the large β2 values can be attributed to the effects of coincidences in the detection beam. These results of the probe operation simulations are decisive because it is the first time coincidence effects in a FSSP have been simulated with the contribution of coincidences of more than two particles. The most surprising result is that coincidences affect significantly the measured size distributions at large sizes, far from the mode. The corresponding values of concentration density are small, less than 2 orders of magnitude smaller than the density at the mode of the distribution, but they are of the same order of magnitude as the concentration density of precipitation embryos that is required for the initiation of the collision-coalescence process. These results imply that such observations of superadiabatic values of the concentration density of large droplets cannot be considered as validated, when measured with FSSP spectrometers. Additional measurements with different techniques are thus required to attest to this phenomenon.
The stochastic simulation of the probe operation is not usable for the inverse procedure, that is, to derive an actual spectrum from a measured one. It has thus been impossible to correct coincidence effects in the measured spectra. The parameterization of DSB by (6) is therefore overestimated. Assuming that large values, which deviate from a normal distribution, are instrumental artifacts, provides a coarse estimation of the bias (7).
7. Conclusions
With the improved size and spatial resolutions of the Fast-FSSP measurements it has been possible to identify very narrow spectra in most of the cloud traverses performed at the upper levels of cumulus clouds during the SCMS experiment. These spectra are much narrower than previously measured with the standard probe. The regions of narrow spectra show characteristics close to the adiabatic reference, such as LWC values slightly lower than the adiabatic value at that level and values of droplet concentration close to the maximum value within the cloud traverse. The spectra observed in these regions are narrow but still broader than the adiabatic reference. The high concentration densities of droplets with diameter smaller than the mode can be attributed to partial evaporation of some droplets resulting from the mixing with dry air. The occurrence of this process is attested by the slightly subadiabatic values of LWC. This feature and the contribution of mixing to DSB will be examined in Part III. At droplet diameters larger than the mode of the spectrum, the values of concentration density higher than in the adiabatic reference (super- adiabatic growth) are more difficult to interpret.
The contribution of the instrument to this broadening has been examined for the first time. A stochastic model of probe operation has been developed. The model is capable of reproducing all types of coincidence events, while the analytical model of Cooper (1988) was limited to coincidence of two particles. The model has been initialized with the reference spectrum and the simulated spectrum has been compared to the observed one. This procedure demonstrates that most of the superadiabatic values can be interpreted as an instrumental artifact, even at a droplet concentration as low as 225 cm−3. It is important to notice that both the FSSP-100 and the Fast-FSSP exhibit the same limitations, as they are based on the same optics. Our conclusion can thus be extended with the same confidence to previous observations of superadiabatic droplet growth with the standard probe. Nevertheless coincidences of particles do not fully account for the difference between the observed spectrum and the reference one.
The β2 scheme has been used to characterize DSB for each selected spectrum by the PDF Ψ(β2) of the integral of S/w. It has been shown that its standard deviation increases linearly with the β2 mean value, as
In this introductory paper, we have demonstrated that regions of narrow spectra, with spatial scales larger than a few hundreds of meters and LWC values close to the adiabatic reference, can be observed as high as 1500 m above cloud base in nonprecipitating cumulus clouds. The narrowest spectra are still broader than reference spectra derived from the idealized model of adiabatic ascent with a uniform field of supersaturation. However, the significant superadiabatic values of concentration density, which could play a crucial role in the onset of precipitation, are likely to be a contribution of the instrument. It is not clear yet if the remaining DSB is the result of microscale heterogeneities, a consequence of mixing, or even the result of an unknown instrumental artifact. The two first hypotheses will be tested in Part II and Part III of the series.
Acknowledgments
The authors acknowledge the support of Météo-France, the National Center for Atmospheric Research, Department of Atmospheric Sciences at the University of Wyoming, INSU under Grant 95317, and the European Commission under Grant ENV4*CT950117. They are particularly grateful to R. Shaw for his constructive comments.
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Spectrum evolution in an adiabatic updraft. (a) Size distribution: f(z0) is the initial spectrum after CCN activation is completed. The curve labeled C is the corresponding spectrum after condensational growth. Curves labeled C + 50 and C − 50 are the resulting spectra for a total droplet concentration of C ± 50 cm−3. (b) Same as (a) for the ϕ2 distributions. Here C = 225 cm−3, z0 = 715 m, P0 = 931 hPa, T0 = 22.3 C, z = 2170 m, T = 16.4 C, ρaΔqA(z0, z) = 3.16 g m−3.
Citation: Journal of the Atmospheric Sciences 58, 6; 10.1175/1520-0469(2001)058<0628:DSBICC>2.0.CO;2
Time series of total droplet number concentration, droplet spectrum represented by its 10% percentiles, and LWC, along a cumulus cloud traverse with the Merlin-IV. The two vertical bars indicate the selection of the adiabatic section. SCMS flight on 15:42: 11.2 UTC 10 Aug 1995 at an altitude of 2188 m.
Citation: Journal of the Atmospheric Sciences 58, 6; 10.1175/1520-0469(2001)058<0628:DSBICC>2.0.CO;2
The ϕ2 distribution (solid line) for the section selected in Fig. 2. Comparison with the adiabatic reference (dot–dashed line); linear scale on top and log scale at the bottom. The initial reference spectrum is represented by a dot–dashed line on the left. Here C0 = 105 cm−3, z0 = 715 m, C = 329 cm−3, z = 2188 m.
Citation: Journal of the Atmospheric Sciences 58, 6; 10.1175/1520-0469(2001)058<0628:DSBICC>2.0.CO;2
Three examples of the comparison between an observed spectrum (dotted line) and the adiabatic reference (dashed line), after instrumental broadening by the Fast-FSSP simulator (solid line). The total droplet number concentrations are, respectively, 225 (a), 329 (b), and 455 cm−3 (c).
Citation: Journal of the Atmospheric Sciences 58, 6; 10.1175/1520-0469(2001)058<0628:DSBICC>2.0.CO;2
PDF of the S/w integral, Ψ(β2), derived from the comparison shown in Fig. 3. The two dashed lines represent normal distributions of the same standard deviation as Ψ(β2) and a standard deviation twice as small.
Citation: Journal of the Atmospheric Sciences 58, 6; 10.1175/1520-0469(2001)058<0628:DSBICC>2.0.CO;2
Comparison between the Ψ(β2) mean value,
Citation: Journal of the Atmospheric Sciences 58, 6; 10.1175/1520-0469(2001)058<0628:DSBICC>2.0.CO;2
The Ψ(β2) standard deviation,
Citation: Journal of the Atmospheric Sciences 58, 6; 10.1175/1520-0469(2001)058<0628:DSBICC>2.0.CO;2
Comparison between the derived standard deviation,
Citation: Journal of the Atmospheric Sciences 58, 6; 10.1175/1520-0469(2001)058<0628:DSBICC>2.0.CO;2
The FSSP is manufactured by Particle Measuring Systems, Boulder, Colorado.
