Characteristics of Cloud Drop Spectra at Different Levels and with Respect to Cloud Thickness

--Measurements on drop size spectra were made in cumulus clouds over Pune (inland) region on many days during the summer monsoon seasons. In this paper, the measurements in non-raining cumulus clouds made in the years 1984, 1985 and 1986 at different levels and for different cloud thickness have been studied. In general, the drop size spectra broadened with height and the concentration of drops with diameter > 50 wm (N_L), mean volume diameter (MVD), liquid water content (LWC) and dispersion increased with height while the concentration of drops with diameter < 20 wm (N_S) and the total concentration of drops (N_T) decreased with height. The average drop size distributions were unimodal at the lower levels while they were bimodal at the higher levels. High water contents were confined to drops in the size range 5-25 wm at both higher and lower levels. The average drop size spectra were broader and N_L, LWC, MVD and dispersion greater while N_T and N_S smaller for thicker clouds (range of vertical extent 1.1-2.1 km) as compared to those for thinner clouds (range of vertical extent 0.3-1.1 km). Water contents for the drops > 28 wm were higher while those for the drops > 28 wm lower in thicker clouds than in thinner clouds. The average drop size distributions were bimodal in the former case, while they were unimodal in the other case.     

基于毫米波雷达、无线电掩星和探空仪资料的云边界高度对比研究

为准确评估基于相对湿度廓线法反演云边界高度的有效性,以CloudSat和CALIPSO联合探测结果为基准,对2008年1月至2009年1月COSMIC无线电掩星和探空仪的云底高与云顶高反演结果进行定量对比验证,结果表明:CloudSat、掩星和探空仪检测到高云的比例差异较大,掩星和探空仪云检测效率相近,但云检测质量掩星优于探空仪,云层沿高度的发生概率同样掩星与CloudSat具有更好的一致性;陆地与海洋地区掩星和探空仪云底高反演精度大于云顶高,且反演精度与云层高度有关,二者对不同类型云的边界高度具有不同的反演优势,云底高发生概率掩星和探空仪与CloudSat都有很好的一致性,但云顶高概率掩星与CloudSat的吻合程度更好;CloudSat云边界高度随纬度升高而减小,其与掩星和探空仪的反演偏差同样是低纬大于中高纬,且具有不同的季节分布特点.此外,三者检测的底层云中低云所占比例从冬季到夏季逐渐减小,顶层云中云顶高于10 km的比例从冬季到夏季却逐渐增加.     

基于毫米波雷达、无线电掩星和探空仪资料的云边界高度对比研究

为准确评估基于相对湿度廓线法反演云边界高度的有效性,以CloudSat和CALIPSO联合探测结果为基准,对2008年1月至2009年1月COSMIC无线电掩星和探空仪的云底高与云顶高反演结果进行定量对比验证,结果表明:CloudSat、掩星和探空仪检测到高云的比例差异较大,掩星和探空仪云检测效率相近,但云检测质量掩星优于探空仪,云层沿高度的发生概率同样掩星与CloudSat具有更好的一致性;陆地与海洋地区掩星和探空仪云底高反演精度大于云顶高,且反演精度与云层高度有关,二者对不同类型云的边界高度具有不同的反演优势,云底高发生概率掩星和探空仪与CloudSat都有很好的一致性,但云顶高概率掩星与CloudSat的吻合程度更好;CloudSat云边界高度随纬度升高而减小,其与掩星和探空仪的反演偏差同样是低纬大于中高纬,且具有不同的季节分布特点.此外,三者检测的底层云中低云所占比例从冬季到夏季逐渐减小,顶层云中云顶高于10 km的比例从冬季到夏季却逐渐增加.     

The coalescence of water drops I. A theoretical model of approaching drops

The approach of two water drops in the absence of air flow around them is theoretically investigated. By assuming deformation criteria it is possible to solve the equation of motion of the drops under the influence of a variety of forces. These forces include the viscous force exerted by the air between the two deformed surfaces, the London-Van Der Waals forces and the force of gravity. It is found that the viscous forces dominate over the whole distance of the interaction. The equations have analytical solutions when a head-on approach is considered and when the deformation of the drops is assumed constant during the interaction. The equations were solved numerically for other deformation criteria and for non head-on approaches.The results of the present model are used in the following paper to compute the coalescence efficiencies of water drops. The model is primarily applicable to situations in which the large drop is stationary and the small one approaches it from below. However, it could also be used for interaction between freely falling drops as long as their relative velocities exceed about 13 cm/sec.Appendix: List of symbols C constant of the motion - D distance between the deformed surfaces of the drops - D _o initial value ofD - D _m the value at which the viscous force is maximum - D _N normalized distance - D _s the distance at which the velocity of approach vanishes - F _c centrifugal force - F _g force due to gravity - F _N normalized viscous force - F _LV force due to London-Van der Waals effect - F _R radial component of the force - F _V viscous force - F _t tangential component of the force - g acceleration due to gravity - M _L mass of large drop - m _s mass of small drop - p ratio of radii of interacting drops - R radius of an arbitrary drop - r distance between the centers of mass of the two drops - R _D radius of deformation - R _L radius of larger drop - R _s radius of smaller drop - t time - u defined in equation 20 — has the meaning of kinetic energy - v relative velocity of the deformed surfaces - v ₀ initial value ofv - V ₀ initial relative velocity of the centers of the drops - V _c critical impact velocity - V _i impact velocity - V _N ,v _n normalized velocity - V _t tangential component of the velocity - W _i velocity of the small drop at infinity for it to reach the pointD ₀ at velocityV ₀ - x instantaneous impact distance -  average critical impact distance for coalescence - x ₀ initial value of the impact distance - x _c critical impact distance for coalescence - coefficient of deformation - _i impact angle according toWhelpdale andList (1971) - coefficient of deformation - viscosity - surface tension - F _s sum of forces acting on the small drop - F _L sum of forces acting on the large drop - time constant - _R Rayleigh's oscillation period On sabbatical leave (1976–77) from the Department of Geophysics and Planetary Sciences, Tel Aviv University, Ramat Aviv, Israel.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Effects of collision-induced breakup on drop size distributions in steady state rainshafts

New equations and techniques for dealing with drop breakups are developed and applied to the modelling of the evolution of raindrop spectra in rainshafts. Breakup experiments byMcTaggart-Cowan andList (1975) served as data base.No matter what the original size distribution, the spectrum evolution will always lead to a Marshall-Palmer type equilibrium di tributionN=N ₀e^–D, with =constant andN ₀ proportional to the rainfall rateR. (D stands for raindrop diameter.) ForR29 mm h^–1 and an original Marshall-Palmer distribution, the required fall height to reach equilibrium is 2 km.The equilibrium distributions are characterized by linear relationships betweenR, the radar reflectivity factorZ, the liquid water content LWC and theN ₀ of the Marshall-Palmer distribution. Possible explanations for the discrepancy with observations are given.The fact that the all-water processes cannot produce drops withD2.5 mm (as confirmed by observations) leads to the conclusion that observed large raindrops withD5 mm represent melted hailstones and have not yet reached an equilibrium distribution. These latter conclusions were reached within the original assumption of videspread, steady state precipitation.     

Die Erforschung der Natürlichen Radioaktivität von Wolkenelementen und einige damit verbundene Probleme

Summary During a number of years at Vilnius the sounding of clouds has been carried out from airplanes in order to study the contents of radioactive materials accumulated in cumuli. Two methods for taking samples have been used: 1) the collection on cooled surfaces and 2) using the method of filter paper covered with erythrosin and kept in a special collector within the Venturi tube. In the first case radioactivity has been measured with the help of Geiger-Müller counter and in the second by means of nuclear photo emulsion (sensitive to -particles) which was brought into contact with the filter paper moistened in the cloud. This method has made it possible: 1) to measure radioactivity in local zones of a cloud, 2) to measure radioactivity of separate big drops and 3) to study the composition of -radioactivity contained in cloud particles.The magnitude of specific radioactivity of cloud elements appears to be of the same order with the rain drops and at times even greater than that of the rain samples.There exist two types of the distribution of radioactivity in a cumulus according to the height: 1) an increase of radioactivity from the bottom to maximum at the height of 0.6 part of the cloud's thickness and 2) two maxima of radioactivity at the bottom and in the centre. The latter phenomenon is characteristic of thick cumuli where big radioactive drops apparently fall out from the centre. The distribution of radioactivity at different heights correlates well with cloud's liquid-water.In a cumulus there takes a place a process of accumulation of radioactive aerosol with the accumulation coefficient of 1000. This circumstance points to a very important part played by clouds as accumulators of radioactive materials from the air which continuously filters itself through them. And just by this is expressed one of the properties of clouds as purifiers of the atmosphere from radioactive aerosol, for, as theoretical calculations indicate, the ability of drops to absorbe radioactive aerosol diminishes with the process of cloud droplets growing to the size of rain drops.The composition of radioactive materials in cloud elements is very complex. In drogs there appear nearly all the natural radioactive elements (emitting -particles) which exist in the earth's crust.     

The role of vibrationally excited nitrogen in the ionosphere

Theoretical and experimental aspects of the production, transformation, diffusion and loss of N₂ in the upper atmosphere are considered. The N₂-CO₂ near-resonant system in theD andE regions is taken into account. We describe our understanding of the methods necessary to find the vibrational populations of N₂ and CO₂ (asymmetric mode of CO₂). The calculations of the vibrational temperatures in theD, E, andF regions for the mid-latitude ionosphere and an aurora are presented. The connection between the excited species and the 4.26-m radiation intensities is considered. The models for the rate coefficient of the reaction of O⁺ with N₂ and the electron density decrease resulting from N₂ in the F region are discussed.     

Observations of condensation growth determined by entity type mixing

It has been speculated for many years that the development of the droplet spectra in cloud is probably influenced by mixing processes. Various theoretical attempts to broaden the droplet spectra by mixing parcels with different velocity histories has shown that that particular effect is small. Similarly, very simpleuniform entrainment procedures did not lead to cloud drop size spectra which were broad enough, although by producing cloud drop size distributions with a double mode these models did substantially improve the drop size spectra of earlier adiabatic models which only exhibited a single mode.Recently a model based on entraining entities representing moving parcels of cloud air within the cloud was detailed byTelford andChai (1980). This study showed that the mixing in of dry air at cumulus turrets could lead to vertical cycling of diluted parcels, and that this cycling, with continual entrainment across the parcel boundaries, will produce much larger drops, as well as smaller drops of all sizes, in the droplet spectra. The entity entrainment concept studied there appears to apply to the observations of stratus cloud discussed in this paper.This paper presents data taken in marine stratus off the California coast which give a particularly clear example of how such droplet spectra modification occurs in practice. Both large drops, and the spread of the spectra to smaller sizes, occur in relation to other variables in such a way as to be consistent with an entity entrainment explanation, with no other obvious possibility.In a marine stratus cloud just over 200 m thick and many tens of miles in extent we find clear evidence that dry air is mixing in at cloud tops. Strong vertical motion is to be found in the cloud, large sized drops are found in cloud parcels where the mixing gives lower droplet concentrations, and there is evidence that newly formed cloud parcels are warmer and contain many more smaller droplets.The observations show that immediately following entrainment of dry air drop diameters are not reduced appreciably, but, in the same parcels, drop concentrations have been reduced by a factor of ten or more. Further down in the cloud big drops, able to start growth by coalescence, are found associated with low total droplet concentrations.Overall, it seems likely from the consideration of these observations that the formation of the large drops which lead to precipitation processes in clouds depends critically on the mixing in of dry air at cloud tops, and very little on the size of the small drops resulting from the condensation nucleus counts. As a conclusion it appears reasonable to state that if entrainment occurs at cloud tops, then big drops will be formed!     

Planar charged-particle trajectories in multipole magnetic fields

This paper provides a complete generalization of the classic result that the radius of curvature () of a charged-particle trajectory confined to the equatorial plane of a magnetic dipole is directly proportional to the cube of the particles equatorial distance () from the dipole (i.e. ³). Comparable results are derived for the radii of curvature of all possible planar chargedparticle trajectories in an individual static magnetic multipole of arbitrary order m and degree n. Such trajectories arise wherever there exists a plane (or planes) such that the multipole magnetic field is locally perpendicular to this plane (or planes), everywhere apart from possibly at a set of magnetic neutral lines. Therefore planar trajectories exist in the equatorial plane of an axisymmetric (m = 0), or zonal, magnetic multipole, provided n is odd: the radius of curvature varies directly as ⁿ⁼². This result reduces to the classic one in the case of a zonal magnetic dipole (n = 1). Planar trajectories exist in 2m meridional planes in the case of the general tesseral (0 < m < n) magnetic multipole. These meridional planes are defined by the 2m roots of the equation cos[m()–_n^m)] = 0, where _n^m = (1/m) arctan (h_n^m/g_n^m); g_n^m and h_n^m denote the spherical harmonic coefficients. Equatorial planar trajectories also exist if (n – m) is odd. The polar axis ( = O,) of a tesseral magnetic multipole is a magnetic neutral line if m > I. A further 2_m(n – m) neutral lines exist at the intersections of the 2_m meridional planes with the (n – m) cones defined by the (n – m) roots of the equation P_n^m(cos ) = 0 in the range 0 < 9 < , where P_n^m(cos ) denotes the associated Legendre function. If (n – m) is odd, one of these cones coincides with the equator and the magnetic field is then perpendicular to the equator everywhere apart from the 2m equatorial neutral lines. The radius of curvature of an equatorial trajectory is directly proportional to ⁿ⁼² and inversely proportional to cos[m(–)]. Since this last expression vanishes at the 2m equatorial neutral ines, the radius of curvature becomes infinitely large as the particle approaches any one of these neutral lines. The radius of curvature of a meridional trajectory is directly proportional to rⁿ⁺², where r denotes radial distance from the multiple, and inversely proportional to P_n^m(cos )/sin . Hence the radius of curvature becomes infinitely large if the particle approaches the polar magnetic neutral ine (m > 1) or any one of the 2m(n – m) neutral ines located at the intersections of the 2m meridional planes with the (n – m) cones. Illustrative particle trajectories, derived by stepwise numerical integration of the exact equations of particle motion, are pressented for low-degree (n 3) magnetic multipoles. These computed particle trajectories clearly demonstrate the non-adiabatic scattering of charged particles at magnetic neutral lines. Brief comments are made on the different regions of phase space defined by regular and irregular trajectories.Also Visiting Reader in Physics, University of Sussex, Falmer, Brighton, BN1 9QH, UK     

The role of wavegroup velocity in the blocking problem

Considering the blocking problem as a baroclinic instability problem in a dispersive wave system with diabatic heating effects, it is of great interest to investigate the role of wavegroup velocityv _gr in blocking processes, becausev _gr controls the energy transfer in the wave field. Using a Newtonian Cooling —type of forcing with a phase differencek to the main field and taking the linearized version of a two-level model, the phase speedc _r, the group velocityv _gr and the growth ratekc _i have been obtained as analytical functions of the mean zonal windU, the thermal windU _T, the coefficient of diabatic heating x, the phase differencek and the wavelengthL. Now the hypothesis is introduced, that a blocking should be expected, ifv _gr has a maximum value in the vicinity ofL _o, for whichc _r vanishes and thee-folding timet=1/kc _i (kc _i>0) is smaller than 6 days (see condition (20) in the text). One finds, that for special parameter combinations (U _T, U, ), where 15 m/secU _T25m/sec,U=10m/sec, 0.8·10^–51.5·10^–5 [sec^–1], certain valuesL _o with an appropriate phase differencek exist, which satisfy the conditions mentioned above (for values see Table 2). TherebyL _o varies within the range 8500 km <L _o<11000 km corresponding to the preferred planetary blocking wavenumber 2 in middle latitudes 50°<<70° N.     

Electromagnetic scattering by a perfectly conducting half-plane in a conductive half-space

FollowingDmitriev (1960) a rigorous theoretical solution for the problem of scattering by a perfectly conducting inclined half-plane buried in a uniform conductive half-space has been obtained for plane wave excitation. The resultant integral equation for the Laplace transform of scattering current in the half-plane is solved numerically by the method of successive approximation. The scattered fields at the surface of the half-space are found by integrating the half-space Green's function over the transform of the scattering current.The effects of depth of burial and inclination, of the half-plane on the scattered fields are studied in detail. An increase in the depth of burial leads to attenuation of the fields. Inclination introduces asymmetry in the field profiles beside affecting its magnitude. Depth of exploration is greater for quadrature component. An interpretation scheme based on a phasor diagram is presented for the VLF-EM method of exploration for rich vein deposits in a conductive terrain.List of symbols x, y, z Space co-ordinates - Half-space conductivity - ₀ Free-space permeability - Excitation frequency (angular) - T Time - h Depth of the half-plane - a Inclination of the half-plane - E _x x-Directed total electric field - E _x ^p x-Directed primary electric field - E _xo ^p x-Directed primary electric field atz=0 directly over the half-plane - H _y y-Component of total magnetic field - H _y ^p y-Component of primary magnetic field - H _y0 ^p y-Component of primary magnetic field atz=0 directly over the half-plane - H _z z-Component of total magnetic field - H _z ^p z-Component of primary magnetic field - J _x Surface density ofx-directed scattering current - G Green's function - k ₀,K Wave numbers - u,u ₀,u ₁,u ₂ Functions - Space co-ordinate - s Variable in transform domain - Variable of integration - Normalized scattering current - Laplace transform of - N Normalized - , ₀, ₁, ₂ Functions - t Variable of integration - Skin depth - H Total magnetic field - H ^p Primary magnetic field - H ₀ ^p Primary magnetic field atz=0 directly over the half-plane - M,Q,R,S,U,V Functions - N ₁,N ₂ Functions     

Inflow and outflow in a rotating circular container—A laboratory model for the Loop Current of the Gulf of Mexico

The Loop Current of the Gulf of Mexico is simulated in the laboratory. A circular tank is filled with water and is placed off-center on a rotating table and the flow field is generated by injecting and withdrawing water at two openings on the wall. The free surface becomes parabolic due to balance of gravitational and centrifugal forces, simulating the latitudinal change of the Coriolis parameter (-effect) in the ocean. The flow characteristics depend on the influx and the rate of rotation and can be classified according to non-dimensional parameters (Rossby, Ekman and Froude numbers denoted byR ₀,E andF, respectively). When the influx is small and the rotation rate is large (smallR ₀,E andF) the flow will be almost linear, and the fluid flows along the side-wall boundary layer under constraint of the -effect. For a very large influx (largeR ₀ andE) inertial forces become very large compared to the Coriolis force and the flow behaves like a potential flow. The flow studied had characteristics between these two extreme cases and hasR ₀ andF similar to the Gulf circulation, though similarity inE is ambiguous. Photographs of the flow indicate that the inflow penetrates further into the interior when the rotation rate is increased while the influx is kept constant. The numerical analysis of the non-linear vorticity equation confirms this for the parameters corresponding to the experiment. In addition, the photographs reveal eddies embedded on both sides of the main stream, particularly near the inflow region. These eddies are intensified and become uniform in size as the influx increases. It is pointed out that such eddies were actually observed near the Loop Current north of the Yucatan Straits.     

The Local Magnitude Scale in the Korean Peninsula

A formula to determine the local magnitude (M_L) following Richters original definition was empirically derived for the Korean Peninsula. A total of 1,644 digital seismograms from 142 Korean earthquakes that occurred from 1997 to 2000 were corrected for instrument response and convolved with the nominal Wood-Anderson torsion seismograph response to be appropriate for the original definition of M_L. Then, the zero-to-peak amplitude was measured in millimeters on the synthetic Wood-Anderson seismogram. Multiple regression analysis was conducted to determine distance and station correction terms for the measured peak amplitudes. The best-fit solution for M_L yielded the following formula for the Korean Peninsula:where A() and S denote the peak amplitude on the synthetic Wood-Anderson seismogram at distance and the station correction term, respectively. Note that the second term, distance correction, was adjusted with Richters M_L, taking into consideration attenuation differences between the Korean Peninsula and southern California, where Richter originally introduced M_L. On average, the magnitudes determined in this study are nearly the same as those determined by the Korea Institute of Geoscience and Mineral Resources (KIGAM), but are larger than those of the Korea Meteorological Administration (KMA) by as much as 0.36.     

Spectral analysis and earthquake scaling of the Petatlan earthquake (M s =7.6) aftershocks,recorded at stations along the pacific coast and between the coast and Mexico City

Spectral parameters have been estimated for 214 Petatlan aftershocks recorded at stations between Petatlan and Mexico City and between Petatlan and Acapulco. The spectral parameters were used to obtain empirical relations for the estimation of seismic moment from coda length and fromM _L . Stress drops, using Brune's model, were calculated for these aftershocks. Six events with large stress drop are located within a previously suggested asperity, and seven more suggest a boundary zone at the intersection of the Petatlan and Zihuatanejo aftershock rupture volumes. Stress drops increase with increasing seismic moment up to 10²⁰ dyne-cm but appear to be constant at greater moment values. The peak horizontal velocity times distance of aftershocks recorded near the coast and between the coast and Mexico City (30 to 270 km away), scales linearly with seismic moment, and predicts well the peak horizontal values of large (M _s 7.0) coastal thrust events recorded on rock sites at Mexico City. Peak horizontal velocity is a straightforward measurement, thus this relation allows us to evaluate expected ground motion between the Pacific coast and Mexico City from the seismic moment of subduction related earthquakes along the coast.     

Determination of characteristics of steam reservoirs by Radon-222 measurements in geothermal fluids

The authors conducted a Rn²²² survey in wells of the Larderello geothermal field (Italy) and observed considerable variations in concentrations. Simple models show that flow-rate plays an important part in the Rn²²² content of each well, as it directly affects the fluid transit time in the reservoirs. Rn²²² has been sampled from two wells of the Serrazzano area during flow-rate drawdown tests. The apparent volume of the steam reservoir of each of these two wells has been estimated from the Rn²²² concentration versus flow-rate curves.List of symbols Q Flow-rate (kg h^–1) - Decay constant of Rn²²² (=7.553×10^–3 h^–1) - Porosity of the reservoir (volume of fluid/volume of rock) - ₁ Density of the fluid in the reservoir (kg m^–3) - ₂ Density of the rock in the reservoir (kg m^–3) - M Stationary mass of fluid filling the reservoir (kg). - E Emanating power of the rock in the reservoir (nCi kg _rock ^–1 h^–1). - P Production rate of Rn²²² in the reservoir: number of atoms of Rn²²² (divided by 1.764×10⁷) transferred by the rock to the mass unit of fluid per unit time (nCi kg _fluid ^–1 h^–1). - N Specific concentration of Rn²²² in the fluid (nCi kg^–1) - Characteristic time of the steam reservoir at maximum flow-rate (=M/Q)     

Determination of source duration and moment of earthquakes in the Indian Peninsula using love waveforms

Love waves recorded by a long-period seismograph at New Delhi (NDI) from seven earthquakes of magnitude 4.3 to 5.2 in Koyna and Bhatsa on the western coast and one earthquake in Ongole on the eastern coast of the Indian Peninsula have been used to determine the seismic moment for each of the earthquakes by waveform modeling. Transverse component of the synthetic seismogram shows that the maximum amplitude of waveform decreases with an increase of source duration. Thus for an evaluation of the seismic moment by equating the amplitude level of the observed and synthetic waveforms, we must know the source duration. The synthetic seismogram also indicates that a short source duration gives rise to a small but sharp pulse and this pulse is interpreted as anLg wave. Comparison of the observed and synthetic waveforms has been used for a simultaneous evaluation of the source duration and seismic moment. The source durations are found to vary between 2.2 and 4.4 s; for earthquakes with a magnitude range between 4.3 and 5.2 these durations are slightly higher than normal. We obtain moment (M ₀) of Ongole earthquake (M _L =5.1)as 1.7×10²⁴ dyne-cm; moments of Koyna and Bhatsa earthquakes (4.3M _L 5.2) on the western coast lie between 0.7×10²³ and 3.6×10²³ dyne-cm. Moment (M ₀)-magnitude (M _L ) relation logM ₀=1.5M _L +16.0 for the western United States region agrees as well, in general, with the results for the earthquakes in the Indian Peninsula.     

The coalescence of water drops II. The coalescence problem and coalescence efficiency

By the use of the model of approaching drops (Arbel and Levin, 1977) the coalescence efficiencies of drops are computed. It is found that for interactions of drops at their terminal velocities the coalescence depends both on the size of the large drop and on the size ratio of the interacting drops in agreement with the experimental results of Whelpdale and List (1971) and Levin and Machnes (1977).The results were found to be sensitive to the assumption of the drops deformation and to the critical separation distance. This distance is defined as the distance at which the drops begin to merge. The variations of the coalescence efficiency with these parameters is discussed.Appendix: List of symbols D distance between the deformed surfaces of the drops - D _o initial value ofD - D _s stop distance, the distance at which the impact velocity vanishes - D _c critical coalescence distance - E collection efficiency - E ₁ collision efficiency - E ₂ coalescence efficiency - E _2R coalescence efficiency for collisions with stationary targets - F _c centrifugal force - p ratio of the radii of the interacting drops - r _o initial distance between drops' centers - R _L radius of larger drop - R _s radius of smaller drop - R _D radius of deformation - v approach velocity of two deformed surfaces - v _o initial value ofv - V _i impact velocity (given negative sign when drops approach each other) - V _c critical impact velocity - W _i velocity of the smaller drop at infinity for it to reachD _o with velocityv _o - x _i impact distance, the distance between the trajectories of the two drops - x _c critical impact distance for coalescence -  average critical impact distance for coalescence - X _c critical impact distance for collisions - coefficient of deformation given in equation 1 - _i impact angle defined byWhelpdale andList (1971) given also inArbel andLevin (1977) - coefficient of deformation given in equation 2 - viscosity of air - _i impact angle used inArbel andLevin (1977) and here - _c critical angle for coalescence - average critical angle for coalescence On sabbatical leave (1976–77) from the Department of Geophysics and Planetary Sciences, Tel Aviv University, Ramat Aviv, Israel.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Total ozone measurements in cloudy weather

Obtaining an accurate, value for total ozone under a cloudy sky, especially when the sun is not high, is a major remaining problem associated with total ozone measurements. The Toronto spectrophotometer has been designed with this in mind. It has been fitted with a polarizing prism, and measures light at four wavelengths simultaneous which makes it possible to obtain two independent double ratios. Clouds produce two effects on ozone measurements; the first is purely an optical effect which causes an apparent increase in ozone, the second is most likely a real increase in ozone associated with large cumulus-type clouds. By considering the three following points it is possible to distinguish between these two cloud effects and probably measure the true total ozone for solar zenith angles less than 80°: 1. The multiply scattered component of polarized light is used to reduce optical cloud variance. This makes all skies appear like thick coulds. 2. A double difference similar to the AD method is used but the two ratios of the double difference are weighted inversely with(= ₁ - ₂ for a pair). This further reduces the optical effects of clouds. 3. Real ozone increases due to large clouds are verified by comparing the increase of ozone obtained from one double difference to that of another. Differences between this multiply, polarized curve and the direct sun curve will be given, and a technique to obtain an accurate value of total ozone under all sky conditions, provided that the solar zenith angle is less than 80°, will be given.     

P-wave spectra of the Füzesgyarmat, eastern Hungary earthquake sequence

On 29–30 September 1996, an earthquake sequence occurred in the Füzesgyarmat region in eastern Hungary. The main shock had a magnitude of M_L = 3.2 and was felt with a maximum intensity 4 MSK. It was preceded by a foreshock with a magnitude of M_L = 2.8 and was followed, within six hours, by five aftershocks with magnitudes 2.1M_L 3.1. The dynamic source parameters of the Füzesgyarmat earthquake sequence have been derived from P-wave spectra of the Hungarian seismograph stations. The average of the obtained values at different stations shows that the main shock occurred on a fault length of 610 m, with relative displacement of 1.13 cm, stress drop of 7 bar and seismic moment of 3.96*10₂₁ dyne.cm. The main shock was small to yield data for a full mechanism solution and no reliable single fault plane solution could be obtained due to the low signal to noise ratio at the recording stations. The parameters of the foreshock are fault length of 560m, seismic moment of 2.09*10₂₁ dyne.cm, stress drop of 5.53 bar and relative displacement of 0.73 cm. The five aftershocks show source parameters similar to the foreshock stress drops (5.26 5.76 bar), fault lengths (415 L 600 m), seismic moments (8.36*10²⁰ M_o 2.31*10₂₁ dyne.cm) and relative displacements (0.52 0.91 cm).     

Scaling of peak ground motions from digital recordings of small earthquakes at Campi Flegrei,southern Italy

The dependence of peak ground acceleration and velocity on seismic moment is studied for a set of small earthquakes (0.7<M _L<3.2) recorded digitally at distances of a few km in the Campi Flegrei volcanic area near Naples, Italy, during the ground uplift episode of 1982–1984. Numerical simulations, using the -square spectral model with constant stress drop and ane ^–kf high frequency decay, fit well both the velocity and acceleration data for an averagek=0.015. The observed ground motions in the 1–24 Hz frequency band appear to consist of radiation from simple sources modified only slightly by attenuation effects. Moreover, the scaling of peak values agrees closely with those determined in nonvolcanic areas, once the difference in stress drop is taken into account.