Drop Size Spectrum Research Articles

Simulations of drop fall in a homogeneous isotropic turbulent flow

Abstract Drop motion in a turbulent flow is studied using a model of homogeneous and isotropic turbulence. The model permits us to generate different realizations of the random velocity field component with given latitudinal and lateral correlation functions and a spatial structure which obeys the Kolmogorov theory. For the generation of the turbulent flow, the structure function of the flow in the form suggested by Batchelor was chosen. This function describes the spectrum of turbulence both in the viscous and inertial subranges. Numerous examples of drop tracks for drops of different size demonstrate a significant influence of turbulence on different aspects of drop (as well as ice and aerosol particle) motion. The tendency of drop tracks to collect along isolated paths is demonstrated. The existence of areas of two types within a turbulent flow is revealed. Drops (aerosol particles) tend to leave the areas of enhanced turbulent flow vorticity and curvature apparently due to their inertia. At the same time, drops tend to “avoid” these areas. Interlacing of the tracks of small drops attributed to different deviations from the velocity of the flow due to the difference in drop inertia is demonstrated. The formation of significant turbulence-induced drop velocity deviations from the air velocity is demonstrated. Some statistical characteristics of drop movement in a turbulent flow are studied using the Monte Carlo method. The analysis of the spectra of relative drop velocity fluctuations reveals a pronounced maximum at frequencies depending on the drop size. The maximum in the horizontal velocity deviation spectra moves from a highest frequency of 20 Hz for a 10 μm drop to about 0.1 Hz for a 500 μm drop. To evaluate the contribution of turbulence (inertia) effects as compared to the effect of gravity, the ratio of root-mean-square drop velocity deviation (induced by turbulence) to the still-air terminal velocity was calculated for a wide spectrum of drop sizes. This ratio reaches its maximum for the smallest drops. Inertial flow acceleration seems to be the main factor leading to the formation of drop velocity deviations from the air velocity. The maximum value of the acceleration for the case considered was greater than 7 g. Possible turbulence effects on the drop spectrum broadening and warm rain formation, generation of drop concentration inhomogeneity and formation of areas of enhanced ice concentration within clouds, time and space inhomogeneity of precipitation rate, in-cloud scavenging rate, and mechanisms of rain enhancement under cloud seeding are discussed.

On the Caltech Active Strand Cloudwater Collectors

A detailed analysis of several versions of the Caltech Active Strand Cloudwater Collector (CASCC) is conducted. Efficiency calculations, design considerations and procedures for cloud liquid water content estimation from the collection rates of these instruments are discussed. The size-fractionating CASCC is capable of simultaneous collection of samples representing two portions of the cloud drop size spectrum. Large drops are collected in an inlet stage while smaller drops are collected in a second stage. Theoretical calculations, which assume no aerodynamic interaction between adjacent rows of collection rods in the inlet, suggest the inlet should have a 50% size cut corresponding to a drop size of 23 μm diameter. However, field test results suggest that focusing of the flow passing through a row of cylinders may increase the efficiency of collection on the subsequent cylinder row, thereby decreasing the overall size cut for the inlet. The CASCC2, a compact version of the original CASCC, is designed to sample the entire cloud drop spectrum. Comparison of the cloudwater collection rates of the CASCC2 and the size-fractionating CASCC showed good agreement when normalized by the flow rate through each collector. The Caltech Heated Rod Cloudwater Collector (CHRCC), designed for use in supercooled clouds, features a theoretical 50% lower size cut corresponding to a drop diameter of 9 μm. Liquid water content values estimated from the CHRCC cloudwater collection rates correlated reasonably well with values measured with a Gerber Particle Volume Monitor (PVM-100) in both warm ( r 2 = 0.83) and supercooled ( r 2 = 0.71) cloud conditions.

Simulations of drop fall in a homogeneous isotropic turbulent flow

Drop motion in a turbulent flow is studied using a model of homogeneous and isotropic turbulence. The model permits us to generate different realizations of the random velocity field component with given latitudinal and lateral correlation functions and a spatial structure which obeys the Kolmogorov theory. For the generation of the turbulent flow, the structure function of the flow in the form suggested by Batchelor was chosen. This function describes the spectrum of turbulence both in the viscous and inertial subranges. Numerous examples of drop tracks for drops of different size demonstrate a significant influence of turbulence on different aspects of drop (as well as ice and aerosol particle) motion. The tendency of drop tracks to collect along isolated paths is demonstrated. The existence of areas of two types within a turbulent flow is revealed. Drops (aerosol particles) tend to leave the areas of enhanced turbulent flow vorticity and curvature apparently due to their inertia. At the same time, drops tend to “avoid” these areas. Interlacing of the tracks of small drops attributed to different deviations from the velocity of the flow due to the difference in drop inertia is demonstrated. The formation of significant turbulence-induced drop velocity deviations from the air velocity is demonstrated. Some statistical characteristics of drop movement in a turbulent flow are studied using the Monte Carlo method. The analysis of the spectra of relative drop velocity fluctuations reveals a pronounced maximum at frequencies depending on the drop size. The maximum in the horizontal velocity deviation spectra moves from a highest frequency of 20 Hz for a 10 μm drop to about 0.1 Hz for a 500 μm drop. To evaluate the contribution of turbulence (inertia) effects as compared to the effect of gravity, the ratio of root-mean-square drop velocity deviation (induced by turbulence) to the still-air terminal velocity was calculated for a wide spectrum of drop sizes. This ratio reaches its maximum for the smallest drops. Inertial flow acceleration seems to be the main factor leading to the formation of drop velocity deviations from the air velocity. The maximum value of the acceleration for the case considered was greater than 7 g. Possible turbulence effects on the drop spectrum broadening and warm rain formation, generation of drop concentration inhomogeneity and formation of areas of enhanced ice concentration within clouds, time and space inhomogeneity of precipitation rate, in-cloud scavenging rate, and mechanisms of rain enhancement under cloud seeding are discussed.

Raindrop Spectra and Updraft Determination by Combining Doppler Radar and Disdrometer

Abstract A new method is presented by which raindrop size spectra are determined from power spectra measured by an X-band Doppler radar. Prior to drop size spectrum calculation, bias caused by vertical wind, vw, is removed by an iterative process that uses a disdrometer-determined relation that is characteristic of the rainfall type. The specific relation (Z ≈ 507 R1.44) is determined from the best correlated data pair formed between Z or w with one of R, M, and vm. The vertical wind is estimated by shifting (rotating) the power spectrum along the velocity axis until this Z-R relation is satisfied. This method works for any shape of drop size spectrum. The power spectrum noise is studied by a computer simulation that indicates that smoothing of the spectra by a running average is not reliable for suppressing stochastic measurement noise. Consequently, a vertically pointing radar scanning strategy was designed to allow averaging of the power spectra prior to drop spectrum calculation. This scan was tested ...

A statistical model of drop-size spectra for stratocumulus clouds

The purpose of this work is to present a simplified model of cloud-droplet spectra that can be used as a tool for interpreting cloud microphysical observations in boundary-layer clouds, and as a way to begin quantifying the couplings between cloud microphysics, dynamics and radiative properties for eventual use in cloud parametrizations. The model is steady-state, ignores nucleation effects, and is formulated to produce horizontally averaged statistics. The major difference between this model and previous work lies in the model assumption that droplet spectra at a given level within a cloud are horizontal averages over a large number of air parcels, each of which can have a different lifting condensation level (LCL). Vertical motions are driven by buoyancy, so that liquid water and vertical velocity are simple functions of height above the LCL. This relationship, treated statistically over a large number of parcels, relates turbulent kinetic energy to horizontally averaged statistics of the droplet spectra. The broadening of droplet spectra is thus directly related to the turbulent kinetic energy within a cloud. In validating the model, results are compared with observations. It is shown that the basic droplet spectra predicted by the model are quite realistic for stratus and stratocumulus. The modelled droplet spectra broaden from cloud base to cloud top as is frequently observed, and the relationship between drop spectrum width and mean radius agrees quite well with observations.

Evidence from Tropical Raindrop Spectra of the Origin of Rain from Stratiform versus Convective Clouds

Abstract An analysis of temporal variations in gamma parameters of raindrop spectra is presented utilizing surface-based observations from the Tropical Ocean Global Atmosphere Couple Ocean-Atmosphere Experiment. An observed dramatic change in the N0 parameter, found to occur during rainfall events with little change in rainfall rate, is suggestive of a transition from rain of convective origin to rain originating from the stratiform portion of tropical systems. An empirical stratiform-convective classification method based on N0 and R (rainfall rate) is presented. Properties of the drop size spectra from the stratiform classification are consistent with micro-physical processes occurring within an aggregation/melting layer aloft, which produces more large raindrops and fewer small to medium size raindrops than rain from the convective classification, at the same rainfall rate. The occurrence of precipitation was found to be 74% (stratiform) and 26% (convective), but total rainfall, on the other hand, was ...

A three-stage cloud impactor for size-resolved measurement of cloud drop chemistry

A new cloud sampler has been designed that is capable of simultaneously collecting three independent portions of the cloud drop size spectrum for chemical analysis. The instrument, known as the IESL cloud impactor, features three jet impaction stages in series, each of which removes droplets above a predetermined cut size. Several interchangeable stages are available, with 50% lower cut sizes of 3, 4, 10, 12, 15, 20, and 30 μm based on drop diameter, permitting numerous combinations of cut sizes to be selected. Calibration experiments indicate the instrument performs according to design. Initial cloudwater samples collected with the impactor at Mt. Mitchell, North Carolina and La Jolla Peak, California reveal ion concentrations in large and small cloud drops higher than those found in intermediate sized drops. The long-term goal for use of the impactor is to evaluate implications of variations in cloud drop chemistry across the drop size spectrum on a variety of processes including aqueous phase sulfur oxidation, precipitation scavenging of pollutants, and pollutant deposition to forests during cloud interception.

Behavior of S(IV) and Formaldehyde in a Chemically Heterogeneous Cloud

Download Hi-Res ImageDownload to MS-PowerPointCite This:Environ. Sci. Technol. 1995, 29, 4, 1023-1031

Simulation of hydrometeor size spectra evolution by water-water, ice-water and ice-ice interactions

Hydrometeors spectra evolution induced by coalescence processes is simulated using a microphysical model of the Berry and Reinhard (1974) type including hydrometeors of seven kinds: water drops, plate-like and columnar crystals, dendrites, snowflakes, graupel and hail. The sensitivity of spectra evolution to several parameters, such as air temperature, drop freezing rate, initial liquid water and ice particles content is studied. The Berry and Reinhard (1974) method was used for numerical integration of corresponding stochastic coalescence equations.A remarkable impact of ice processes on the evolution of hydrometeors of all types is demonstrated. The amount of large droplets in mixed phase experiments is significantly less than that in the experiment without the ice phase. The main factor causing the cessation of water spectrum broadening is connected with a crucial decrease of the coalescence rate between water droplets due to permanent elimination of the largest droplets from the drop spectrum as a result of ice-water interaction and drop freezing.The results of simulations show that when only coalescence processes are considered, relative amounts of snowflakes and graupel crucially depend on air temperature. Under comparably high temperatures it is snowflakes that are the dominating hydrometeor type, while under low temperatures graupel can be the dominating hydrometeor type due to an increased rate of drop freezing. A high sensitivity of snowflake/graupel content ratio to the initial size of crystals is demonstrated. Initial liquid water content in model experiments appears to be one of the most important factors determining the formation not only of graupel, but of snowflakes as well. Results indicate the existence of a “critical” minimum concentration of water drops and minimum broadness of the drop size spectrum, which means that when the corresponding values are smaller there is no large snowflake or graupel generation.

Drop Inertia and Its Contribution to Turbulent Coalescence in Convective Clouds. Part I: Drop Fall in the Flow with Random Horizontal Velocity

Abstract The results of simulated drop fall in horizontal flows with the vertical shear of different kinds (constant linear, periodic, and with random velocity distribution) are presented. It is shown that the inertia of drops is significant enough to lead to substantial drop velocity deviations from the velocity of the flow and to the generation of relative velocity between drops of different sizes. For small droplet the velocity difference caused by turbulence is of the same order as the difference in terminal fall velocities. The results of calculations of drop fall through the horizontal flow with the random Kolmogorov spectrum distribution of velocity indicate that a comparable impact of turbulence in this flow is significant for the whole spectrum of drop sizes and that it even increases for small droplets. The increase of the relative velocity between interacting drops is interpreted as an increase in the swept volume and an increase of a number of drop collisions per unit of times. Thus, in the co...

Acidity variations across the cloud drop size spectrum and their influence on rates of atmospheric sulfate production

Measurements of pH variations within natural cloud drop populations reveal that small drops are often more acidic than large drops. Cloud samples collected from coastal stratus clouds, frontal clouds, and radiation fogs, from heavily polluted and pristine locations, had pH values ranging from below three to more than seven. Differences between small and large cloud drop acidities as large as two pH units were observed, although differences were generally below one pH unit. This chemical heterogeneity can significantly enhance oxidation of sulfur dioxide to sulfate within clouds, relative to oxidation rates predicted from the average cloudwater composition. One‐third of the sampled clouds were estimated to experience an increase of at least 20% in the rate of sulfur oxidation by ozone (8% of the clouds had increases exceeding 100%) as a result of acidity differences between large and small cloud drops. These findings suggest that sulfate production within clouds, a critical component of the global sulfur cycle, may be more rapid than previously thought.

Corrections to empirical relations derived from rainfall disdrometer data for effects due to drop size distribution truncation

A description is given of methods by which empirical relations may be corrected for the effects of drop size distribution truncation. Empirical relations derived from experimental drop size spectra are used to demonstrate these effects. It is shown that the most accurate method of performing these corrections involves the assumption of a gamma drop size distribution and a correction applied to each of the experimental spectra. In lieu of this approach, the correction may be applied post hoc provided a priori knowledge of the drop size distribution shape is available.

Drop-size Spectra and Deposits of Four Bacillus Thuringiensis Formulations on Simulated and Natural Fir Foliage

In aerial spray studies reported in the literature using concentrated aqueous formulations, the segments of drops that remained above the foliar surface were sized after impaction. The drop volume that could have penetrated into the foliar cuticle was not taken into account. The objectives of the present study were to spray monodispersed drops over natural and simulated balsam fir needles, to determine drop spreading, to measure the sizes of drop segments above the foliage, and to compute the drop volume that penetrated into the foliar surface. Four aqueous formulations of Bacillus thuringiensis var. kurstaki, containing a dye and a chemical tracer [triethyl phosphate (TEP)], were sprayed in a laboratory chamber over balsam fir branches clipped from field-grown trees. Spray was also applied on aluminum fir branches with and without a coating of the cuticular wax extracted from natural fir foliage. Drop-size spectra, drops/cm2, and deposits (ng TEP/cm2 of foliar area, and ng formulation protein/cm2) were assessed on the natural foliage and wax-coated aluminum foliage (foliar simulator); but only drops/cm2 and deposits of TEP and protein were measured on the uncoated aluminum foliage. Both natural foliage and foliar simulator received similar drop sizes, drops/cm2, and deposits, but the latter two parameters were higher on the uncoated aluminum foliage. The investigation provided a new method to determine the actual sizes of drops deposited on a foliar simulator. The simulator not only had similar size and shape, but also the same surface characteristics. Quantification of protein deposits was also faster on the simulator than on the natural foliage.

Drop size modification by forest canopies: Measurements using a disdrometer

The modification of the drop size spectra of natural and simulated rainfall by the canopies of three tropical plantation tree species was measured using a disdrometer. Contrary to previously published results, large differences were found between species in the degrees of modification. The median‐volume drop diameters measured were 2.3, 2.8, and 4,2 mm for Pinus caribaea, Eucalyptus camaldulensis, and Tectona grandis, respectively. The characteristic drip spectra for the different species are equivalent to the corresponding drop size spectra for rainfall with approximate intensities of 50, 100, and 3000 mm h−1 (essentially infinite) for P. caribaea, E. camaldulensis, and T. grandis, respectively. These results have implications for the choice of the best tree species for areas susceptible to soil erosion.

Mass transfer in a bottom blowing cold model converter

In a model converter containing oil and water the volumetric mass transfer of caprylic acid was determined in dependence of the gas flow rate. Several other parameters were varied such as the number and configuration of nozzles, gas velocity, oil viscosity and volume and model size. Partially the results could be described by dimensionless equations. Visual observations of the bath surface with special regard to the wave formation complete the results of the measurements. By knowledge of the drop size spectrum independently determined, the mass transfer coefficient under dispersion conditions could be evaluated. These values were compared with mass transfer coefficients which had been directly measured by the single rising drop technique as well as the bubble stirred interface without dispersion. It seems that turbulence in dispersed systems does not enlarge the mass transfer coefficient.

CLOUD DROP SPECTRA IN MARITIME AND INLAND REGIONS

Measurements o f clo ud drop ..ire spectra on non-preci pitating cumulus clouds, 1·2 km thick,were made at differe nt levels o ver the Arabian Sea (maritime) and over r une (inland) regio n during the end ofthe summer monsoo n seasons of 1973, 1974 and 1979.The macimurn size of clo ud drops for the. Arabian Sea generally increased with height. while that for run eJiJ not show a systematic change with height. At bot h the local ions. the total concentration o f drops decreasedwith height. The maritime dist ributions were bimodal at all levels while those o..-er Punc were usually unimodal.The average values of liquid water content. mean vo lume diameter. dispersion and conccnt rarion of drops withdiameter > 50 «m were a lin le greater and total concentration a little smaller over the maritime region as ' om'pared to those over inland. The co ncentrations of drops with diameter < 14 ,...m and those > 78 I'm and thema ximum ~ i 7e were greater over Pune than o..er the sea. The ..'a riarions in cloud drop spectra and the clo udphysical parameters over beth the locations are discussed.Kc) words - Cloud drop size spectra, Drop co ncentration,

Effects of Drop-Size-Distribution Truncation on Computer Simulations of Dual-Measurement Radar Methods

Abstract An investigation is made of the effects of truncating the raindrop-size distribution at minimum and maximum diameters on the results of computer simulations of dual-measurement radar methods. The dual-measurement methods investigated include those that involve the pairs of measurables (Z, A), (A, Σ), (ZDR, ZH), and (vZ, Z), where Z, A, Σ, ZDR, ZH, and vz are the Rayleigh reflectivity factor, microwave attenuation, optical extinction, differential reflectivity, Mie reflectivity factor at horizontal polarization, and mean Doppler fall speed, respectively. It is found that the systematic offsets of calculated versus actual values of rainfall parameters observed in previous work using experimental disdrometer drop-size spectra can be attributed almost entirely to truncation effects. Any remaining offset after truncation effects have been removed can be attributed to deviations of the drop-size distribution from exponentiality. The effects of truncation on empirical relations deduced from experimental...

Algorithms for Determination of Rainfall Integral Parameters Using Reflectivity Factor and Mean Doppler Fall Speed at Vertical Incidence

Abstract Algorithms are presented that can be used to deduce rainfall integral parameters from mean Doppler velocity and reflectivity factor at vertical incidence. Simulations are performed using experimental drop-size spectra to test the accuracy of the algorithms, as well as their sensitivity to variations in the form of the drop-size distribution. It is found from these simulations that the method produces results that are very similar to those found using other dual-measurement algorithms, such as those involving the combinations (Z, A), (Z, Σ), and (ZDR, Z) where Z, A, Σ, and ZDR are the reflectivity factor, microwave attenuation, optical extinction, and differential reflectivity, respectively. However, to realize the maximum potential accuracy of the method, a reliable means of estimating the vertical winds must he available, or the measurements must be made close to the earth's surface where such effect arc minimal. An analysis is performed of the errors in integral parameters due to the presence o...

Drop Size Spectra and Deposit from Aerial Spraying With and Without a Polymeric Adjuvant

In a study reported in the literature, an aqueous solution of a polymer, Sta-Put, was shown to increase the drop sizes of the spray cloud when atomized using hydraulic nozzles in an airstream (speed, 192 km/h) under laboratory conditions. The objective of the present study was to examine if Sta-Put can influence the drop size spectra of the spray cloud under field conditions when applied through rotary atomizers using a fixed-wing aircraft flying at a speed of 160 km/h. Tank mixes were sprayed aerially with and without Sta-Put. Size spectra of drops were measured at the target site on Kromekote cards. Deposits were assessed on balsam fir-shaped aluminum branch tips, natural fir needles, and glass plates.

An Improved Raindrop Chemistry Spectrometer

Abstract A spectrometer allowing size-fractional chemical analysis of raindrops has been described previously by the authors. Modifications to this raindrop chemistry spectrometer now allow improved performance in windy conditions. Instrument verifications show that drop-size distribution parameters can be estimated to 2%, and pH versus drop-size spectra can be obtained to 0.02 pH units in wind speeds up to 3 m s−1. Improved resolution will allow trace chemical analysis for comparison with detailed rain chemistry models.