Introduction

In many cases, convective precipitation development through collision-coalescence can be thought of as a two stage process involving production of large embryos that have the potential to grow into raindrops, and the subsequent growth of this embryos to precipitable sizes. There are many different ways in which large drops can be created or introduced into convective clouds. The existence of the embryos however does not necessarily mean that the cloud will develop precipitation. Some clouds have lifetimes that are too short to permit precipitation development, while others entrain so much dry air that they simply do not have enough liquid water to fuel raindrop production. In order to enhance collision-coalescence and the ice process, cloud seeding techniques have been developed over the years, in which the main feature is the introduction of material that can act as cloud condensation nuclei or ice nuclei. And from there, enhance processes like the collision-coalescence described above, and the ice growth process. The most common "seeding agent" known is Silver Iodide, used to promote the ice nucleation process. Mather et al (1991), while conducting measurements, in a cloud that was developing over a paper mill, found that the sampled cloud indicate an enhancement of the coalescence processes, due to the presence of hygroscopic material form the paper mill. Based on these measurements a seeding technique was developed using hygroscopic material form a flare burned on an aircraft and dispersing the seeding material at cloud base level. The composition of the flare is similar to the plume, whose particles are composed of Na₂SO₄, NH₄HSO₃, Ca (HSO₃) ₂, NaOH, Na₂SO₃ and H₂SO₄. The variation for the flare was the introduction of Mg as a burning agent to produce a small hygroscopic particle that will act as a cloud condensation nuclei (CCN). This seeding technique is currently been tested in Monclova Coahuila, northern province in Mexico. This paper will focus on the microphysical conditions necessary to support effective coalescence growth via a cloud seeding technique using hygroscopic material. More specifically, this paper will examine the development of rain in warm convective clouds (which are the clouds that has been sampled in Monclova) suggesting a quantitative threshold for the onset of effective coalescence growth enhanced for the seeding material. In addition on some of the implications of such thresholds on our understanding of cloud structure and evolution, different flare compositions and size distributions, will be used to simulate simultaneous condensation and coalescence processes, to explore how hygroscopic seeding below cloud base might affect the initiation of coalescence and the production of rain. If the seeding particles are smaller than natural cloud condensation nuclei; they will not be activated and will have no effect. If the are much larger than the natural CCN, they may provide embryos on which raindrops can form. However, for the cases where the CCN are comparable to or slightly larger than natural CCN, the consequences are less certain. If the added particles simply modify the natural CCN population to one with similar sizes but higher concentrations, smaller and more numerous droplets would be expected and coalescence would be slower.

Calculations of the expected rates of coalescence are used to illustrate the possibility that hygroscopic seeding might accelerate coalescence. This study emphasizes particles having diameters of 0.3 - 1mm because this appears to be the important range of sizes produced by the seeding flares. These particles are much larger than most natural CCN, and hence will activate first, thus participating in the determination of the droplet size distribution at cloud base. The result can be a broadened droplet size distribution, larger drops more favorable to coalescence and sometimes lower initial droplet concentrations in the seeded cases.
 
 
 

Fig 1. Four examples of measured particle number, for the different flare compositions.

 

The seeding material produced by flares

The size distribution of particles to be used for the calculations in this paper is shown in Fig.1. The measurement were made using a passive cavity aerosol spectrometer probe (PCASP) and a forward scattering spectrometer probe (FSSP), both manufactured by Particle Measuring systems, Inc. For these measurements an aircraft equipped with these two probes was flown about 50 m behind a seeding aircraft that was burning two of the flares. Both aircrafts were flying approximately at the same speed so airspeed corrections to the FSSP measurements were not large. The FSSP-300 spectra is shown in the figures in a black line; the PCASP spectra is shown in the figures in a red line, while the thick blue line is the fit for the two measurements. Four different flare compositions were to be tested. The new Aluminum flare, the normal South African flare, an organic based French flare and a variation of the South African flare. The particle size distribution where measured (Fig. 1) and due to a lack of time, only the French flare was used for the calculations.

The different aerosol spectrometers often do not agree in regions where they overlap. In particular, the PCAS often exhibits elevated counts in the 2-3mm range compared to the others instruments. The cause of this is unknown. In this case we will use a smooth spline to connect the data between the PCAS and the FSSP-300. For the majority of the samples the fine-mode concentrations were so large that errors incurred in the narrow size range should be relatively small. In order to fit a line between the two probes, a table with new bin sizes as a form of average between the overlapped area was constructed (table 1), Figure 2 shows the particle normalized distributions for the four flare compositions. Is necessary to fit a log normal distribution on the data, and the parameter obtained from here will be used as an input parameter in the modeling.

There is a lot of interest on the French flare, since is clear on the figures that is showing particles with bigger sizes, and concentrations higher than the other flares, so the first flare that will be working is the French flare (it will be the only one mention here in terms of calculations, and input parameters for the model).

The size distribution for the French flare showed in Fig 2. can be approximated by the sum of two or three lognormal distributions. Table 2 shows the routine used in MATLAB to calculate the log normal distribution of the French flare. The size distribution showed in figure 2 for the French flare can be approximated by the sum of two or three lognormal distributions. Figure 3 show that sum.

The French flare showed the following data:

m₁= 0.249x10^-4s_{1= 0.3} Concentration₁ = 96

m₂= 0.85x10^-4s_{2= 0.4} Concentration₂ = 0.0215

m₃= 3.8x10^-4s_{3= 0.6} Concentration₃ = 1.32x10^-5
 

Table 1. Normalized size distributions and the new averaged bins for the different flare compositions for the two probes (FSSP-300 and PCASP).

 
 

Fig. 2. Normalized size distributions. The data is showing the averaged sizes distributions for the different flare compositions as shown in Fig. 2. This is comparison of the spectra produced by the different flares.

 
 
 
 

Table 2. Error and Functions used to calculate the log normal distributions for the flares.

Fig. 3 Log normal distribution of the French flare.

 

Numerical approach

The calculations used in this paper represent the effects of condensation and coalescence during adiabatic ascent of a closed parcel. In such calculation, reassignment of droplets to categories or "bins" during the calculation can lead to an artificial broadening of the droplet size distribution, so growth by condensation was treated by allowing the size assigned to each bin to change without any reassignment of droplets to new bins. This avoids the need for interpolation among the bins and so permits very accurate calculation of the initial size distribution.

The procedure of the model is as follows:

Name of the program: growlr (Leighton-Rogers growth) calculates simultaneous condensation and coalescence growth including activation of CCN.

Method:

1. "howl" technique for activation and condensation growth.

2. Modified Kovetz-Olund coalescence (modified to allow category of drops to grow to conserve mass, rather than interpolate between categories). Tests indicate that this is better than interpolation at either large-drop or small-drop sizes. Interp at large-drop size: too-fast growth of largest drops; at small-size, doesn't allow continuous-collection effects of largest drops with small cloud droplets.

3. The size arrays are indexed by decreasing size, to permit addition of droplets at small size while preserving monotonic ordering for interpolation. (Historical; no longer used)

4. The array is initialized with logarithmically decreasing sizes, then sizes are adjusted during growth: All condensation is via changes in bin sizes, while coalescence redistributes drops among bins but also changes bin sizes to conserve mass. This preserves high size resolution needed for condensation and avoids broadening caused by interpolation for condensation growth.

5. Uses a single array to combine droplets from natural and seeded CCN. On activation, saves mass of salt and type of salt. At growth, uses salt mass and type. For coalescence, calculates salt mass and type in new droplets, adds as an average to drop category of product drops. This makes it possible to trace the chemistry of the drops, to some extent. INPUT: (normally in input file growlr.in" see Table 3)

Fig 4. CCN activation spectra, taken at cloud base level, this is assumed to be the natural CCN activation spectra for the region of Monclova Coahuila Mexico.

Table 3. Input file growlr.in

Representation of the CCN spectrum

The warm microphysical processes include: activation of CCN, condensation and evaporation, collision coalescence, and breakup, the number of drops that can be activated at a certain supersaturation was determined by CCN activation spectra in the form:

Where N is the number of drops that could be activated at supersaturation S (%) with respect to water and C and k are empirical parameters (different for continental and maritime clouds).

The CCN activity distribution as function of supersaturation used in this paper is for the Monclova area (north of Mexico). The measured distributions could be represented approximately by the values C=1007.35 cm^-3 and k = 0.5735. The CCN distributions to be used for seeded and unseeded cases are shown in Fig. 4; this data was taken at cloud base level on July 07 1998. As mention before the seeded material was assumed to have the size distribution shown in Fig. 3 except that the measured concentration was reduced by a factor of 100 for the small particles, 1000 for the medium size particles, and 10000 for the biggest particles to allow for dilution before the plume entered cloud base.

Two CCN distributions to be used for the seeded and unseeded cases are shown in Fig 5, one for the natural CCN and the other one for the natural CCN plus the seeded material. While some natural giant particles where included, the total concentration with diameters larger than 10 mm was only about 0.1 m-3. Figure 5 underestimates the concentration of particles in the 10-100mm range, all particles are assumed soluble, so some adjustment to the measured size distributions of (mostly insoluble) particles is needed. This is other aspect that must be studied, is necessary to do some evaluation of the effects of higher background concentrations of giant particles in order to understand the effect of this large particles, and its concentration. Since the FSSP-300 and the PCAS probe are incapable of measuring large particles, and this is very important for this kind of studies and this will be shown later in some early results.

Diffusional growth

Berry’s (1967) calculations of droplet growth by collection showed the effects of a variety of collection kernels on a single initial distribution. The calculations of Barlett (1966) showed that the distributions having larger droplets develop faster than those having fewer larger droplets. Berry (1968) noted similar effects somewhat more quantitatively. However because of the difficulty in constructing numerical methods sound enough to solve the stochastic collection equation with sufficient accuracy in its more unstable modes, reliable quantitative calculations were not available over a wide range of initial conditions. Very accurate numerical methods have now been developed, and the growth by collection of a variety of initial droplet distributions has been re-calculated. In this paper the calculations were followed in the following context: Once activated, droplets were assumed to grow in accord with the Fukuta and Walter (1970) representation of the droplet growth equation with an assumed condensation coefficient of 0.04 and an accommodation coefficient of 1.0.
 
 

Natural	Natural
Seeded case	Seeded case
Fig 5. Cumulative concentrations of CCN as a function of supersaturation for natural and seeded cases representing continental conditions.

 

The mass of solute in the original CCN was used at each step to calculate the growth rate because (especially for the seeded CCN) this mass was large enough to influence the growth rate while supersaturation maximum was approached near cloud base. Natural and seeded CCN were taken to be ammonium sulfate and potassium chloride, respectively. Growth by condensation was represented by increasing the mass assigned to each bin, so all droplets in each bin grew at the same rate. The growth calculations also included the effects of solute concentration on the surface tension, the activity coefficient, and the density of the solution.

Another improvement of this technique is the implementation of the different flare compositions, just to make it simple and because of the lack of time, the calculations were done using the same chemical composition that was mentioned before, but in the future a more detailed chemistry will be used for the different flares.

Supersaturation

Water vapor was used as the prognostic variable, and temperature was diagnosed using the assumption that ascent was adiabatic. Specifically, the interaction between supersaturation and temperature was incorporated by calculating the wet-equivalent potential temperature at cloud base, then using the conservation of this quantity and of the total mixing ratio during adiabatic processes to calculate subsequent temperatures from the vapor pressure.

Coalescence

The major difficulty in the present model, is the development of a useful quantitative measurement of the meaning of the term ‘effective growth. First of all, effective growth must be rapid, because convective clouds can be short lived; an active coalescence process must be able to form precipitation-sized drops within a cloud lifetime or perhaps 30-40 minutes. Secondly, effective growth must mean that the average growth rates are large. Statistical arguments about ‘most-favored’ or ‘fortunate’ particles being able to grow somewhat faster than average can be of considerable importance concerning the spreading of the main peak in a droplet distribution. These effects are most important when the particle interactions are infrequent and the mean growth rates are too slow. Once particles begin to grow rapidly through collision-coalescence, however, the process becomes unstable, and the growth rates are so large that statistical arguments are not necessary. In this model, to be compatible with the variable bin sizes used to represent condensation, a modified Kovets and Olund (1969) scheme was used. The Kovets and Olund algorithm assigns drops resulting from collisions to the two bins bracketing the correct size, in proportion chosen to conserve mass in the collision. This leads to some acceleration of the growth of the largest drops, because the interpolation distributes the resulting mass between two adjacent bins and so leads to numerical broadening of the size distribution. Instead if interpolating between the bins bracketing the correct size of the drop resulting from a collision, drops were assigned to the bin nearest to the correct size, but the average size assigned to that bin was then modified to conserve mass.

A significant deficiency in the approach taken here is that sedimentation is not included (except to the extent that the collision kernel depends on the different fall speeds of the colliding drops). This leads to quite unrealistic results by the time the calculations ends because millimeter-size drops have formed that have fall speeds comparable to the assumed updrafts. This same weakness applies to many other standard coalescence calculations. Because the objective is to determine if the warm-rain process can be accelerated by hygroscopic seeding, we rely only on qualitative conclusions; the quantitative results require considerable interpretation to compensate for this and other weaknesses of a closed parcel model. Typical integration used time steps of 0.1 s or smaller near cloud base, and 1-10s(depending on updraft profile) one the parcel rose more than 100 m above cloud base. Mass conservation was enforced by the selected calculation scheme, so changes in total water substance could result only from numerical rounding. Water substance was normally conserved to better that 1x10^-5 relative error.
 

Fig. 6. Sounding of Monclova 980721

 

Sounding and CCN distributions

A temperature sounding (Figure 6) from Monclova Coahuila Mexico was used for levels below 400 mb, but above 400 mb the sounding was modified by the introduction of and artificial stable layer to inhibit any further ascent. Cloud base pressure was 690 mb where the temperature was 10.5 ^oC. In this sounding a parcel was allowed to rise as driven by buoyancy from cloud base (with an initial cloud base updraft of 3m/s) until the again the parcel reached zero vertical velocity about 1700m above cloud base and 3 min after passage through cloud base.

Even though the parcel was negatively buoyant at the level when it stopped rising, the parcel was then arbitrarily held at this level to provide a total growth time of 900 sec after passage through cloud base. In these calculations, "unseeded" conditions were represented by the natural CCN spectrum shown in Fig 4. To suppress possible effects of giant CCN, the slope of the size distributions for CCN with diameters larger than about 1mm was assumed to decrease in proportion to r^-9, where r is the particle radius.

The resulting parameters for a parcel rising on this environment is presented in Fig. 6, here is clear the changes that such parcel of air is suffering. Is clear the development of such parcel form the different parameters plotted.
 

Fig. 7 History of the liquid water content (LWC g m-3), temperature (T oC), updraft (W, m s-1), and altitude above cloud base Z(m) for a parcel rising on the sounding on Fig. 5

Fig. 8. Mass distribution at 20, 600, 750 and 900 s for the background

Effect of the seeding material from the flares

Figure 9 shows the result when the preceding conditions, are modified by the addition of seeding material in a concentration of 96 cm^-3; with the size distributions shown in Fig 3. The initial cloud base size distribution in the seeded case was slightly broader and extended to significantly larger sizes than in the unseeded case. Drizzle droplets appeared in high concentrations. After 600 seconds the calculations that included the largest particles, converted a larger amount of the condensate to rain drop sizes. Is clear the change of the background spectra, as the different particles are added to the background distribution, the concentration of raindrops increase. And when the three size distributions are added together the spectra changes in a very significant way, this is indicating that bigger particles are very important, and is necessary to study more about the effect of this bigger particles on the evolution of the size distribution.
 

Fig. 9. Mass distributions for the seeded case.

Figure 10 shows the drop concentrations, using the natural CCN as a background. Is clear that the addition of the first size distribution, lows the drop concentrations, because more drops were converted to precipitable size, so the concentrations of droplets lowers significantly. Now when the second and the third size distributions are included in the model, a considerable drop in the droplet concentration is present, this also proves that big particles really affect the size distribution of clouds.
 

Fig 10. Drop concentration produced by the French flare. Background concentrations plus the seeded particles are plotted here as a function of time.

Fig. 11. Same as figure 10. A closer look at the different drop concentration, when a seeded particle is used.

Discussion

These results where constructed to exaggerate any seeding effects. The purpose of these calculations, is to illustrate that hygroscopic material from flares, might have a beneficial effect on precipitation development, through either of two distinct mechanisms: 1) introduction of embryos to enhance coalescence, as in conventional hygroscopic seeding; or 2) broadening of the initial droplet size distributions resulting in acceleration of all stages of the coalescence process.

The different flare compositions are to be compared in the near future, and how such flares are affecting the droplet size distributions. And eventually it will be possible to understand how the big particles from the flare are affecting the initial drop size distribution.

Conclusions

It is well established that higher initial droplet concentrations tend to inhibit coalescence, and also that some very large CCN can be beneficial. Concentrations of such large CCN found to be beneficial for seeding in this model. The calculated effects of seeding with hygroscopic flares suggest that the formation of precipitation via coalescence might be accelerated by such seeding, so this results support the preliminary results found in the cloud seeding program in Mexico. However, the results presented here should be interpreted with considerable caution because they over simplify the real process of precipitation formation.
 

Future work involves the study of the others flares in the rain process, click here to see the latest plots from the numerical modelling.