Measurement of lower-stratospheric aerosol by a balloon-borne photometer

Height distribution of the stratospheric aerosol extinction coefficient was measured in the altitude range 10 to 20 km by a balloon-borne multi-color sunphotometer in May 1978. It is demonstrated that detailed structures of the distribution of stratospheric aerosol can be remotely measured by the solar occultation method as well as by lidar andin situ particle counter observations. In the aerosol layer appearing at 18 km altitude the extinction coefficient at 800–1000 nm wavelength reached to 3×10^–7 m^–1, which was reasonable compared with lidar observations. Wavelength dependence of the aerosol optical depth was crudely estimated to be proportional to ^–1.5.     

Interaction of trace metals with natural particle surfaces: Comparison between adsorption experiments and field measurements

The distribution of the metal ions Zn and Pb between particulate and dissolved phase in river Glatt was studied by field measurements and compared with calculated simulations, using parameters obtained by adsorption experiments with natural suspended particulate material. Differences in distribution coefficients obtained from field data are observed in function of the sampling locations and of the composition of the particulate matter.Experiments in which metal ion solutions are titrated with a suspension of natural particles and analyzed by anodic stripping voltammetry, are interpreted in terms of binding capacities and conditional stability constants of Zn and Pb with the surface sites. Binding constants of a particular metal ion varied very little for all samples. We obtained mean values for the conditional average complex formation constants at pH 8 of: log^cond K _Pb = 9.44 ± 0.18 and log^cond K _Zn = 8.17 ± 0.20. At this pH, binding capacities of 5 10^–3 – 1.7 10^–2 mol/kg of particles were obtained for samples collected at different locations and times; organic material, iron and manganese oxides are considered to be the main components that control the adsorption to the particles.Distribution coefficients are calculated from the experimentally obtained binding capacities and conditional stability constants. Calculated distribution coefficients for Zn agree with those obtained from the field data and are not very sensitive to changes in the composition of the solution. Good agreement was obtained for lead as well; for some samples it was important to take two types of sites with different affinity into consideration.     

Charge distribution on the atmospheric aerosol over the North Atlantic and the Indian Ocean

The distribution of electric charge on the marine aerosol was determined near the sea surface of the Indian Ocean and the North Atlantic during the final stage of the Snellius II-expedition. Mean values for small ion concentrationsn ⁺=455 cm^–3 andn ^–=340 cm^–3 were found over the Atlantic, whilen ⁺=310 andn ^–=250 cm^–3 were the mean values over the Indian Ocean. The ration ⁺/n^– increased from 1.2 to 2.0 with decreasing wind velocity. At wind velocities below 5 m/s 75% of the net space charge near the ocean surface was found to be carried by small ions.     

Influence of ion attachment on the vertical distribution of the electric field and charge density below a thunderstorm

A numerical model called PICASSO [Production d’Ions Corona Au Sol Sous Orage (French) and Production of Corona Ions at the Ground Beneath Thundercloud (English)], previously designed, is used to describe the evolution of the principal electrical parameters below a thunderstorm, taking into account the major part played by corona ions. In order to improve the model restitution of a real situation, various improvements are performed: an initial vertical distribution of aerosol particles is introduced instead of the previously used uniform concentration; time and space calculation steps are adjusted according to the electric field variation rate; the upper boundary condition is improved; and the coefficients of ion attachment are reconsidered with an exhaustive bibliographic study. The influence of the ion attachment on aerosol particles, on the electric field and charge density aloft, is studied by using three different initial aerosol particle concentrations at ground level and two types of initial vertical distributions: uniform and non-uniform. The comparison between field data and model results leads to adjust the initial aerosol particle concentration over the experimental site at the value of 5000 cm⁻³ which appears to be highly realistic. The evolutions of the electric field and of the charge density at altitude are greatly influenced by the aerosol concentration. On the contrary, the surface intrinsic field, defined as the electric field that would exist underneath a thundercloud if there were no local charges, is weakly affected when the model is forced by the surface field. A good correlation appears between the success in the triggered lightning attempts and this intrinsic field evaluation. Therefore, when only the surface field is available, the model can be used in a triggered lightning experiment.     

Turbulent “Dynamo” in the Passive Scalar Problem

A turbulent magnetic dynamo can be considered as the evolution of a vector field in a turbulent fluid flow. The problem of evolution of scalar fields (e.g., number density of small particles) in a turbulent fluid flow is similar to the turbulent magnetic dynamo. The dynamo instability results in generation of magnetic field. The most important effect which can cause a generation of mean magnetic field in a turbulent fluid flow is the -effect: = – (1/3) u · ( × u), where u is the turbulent velocity field with the correlation time . A similar instability in the passive scalar problem results in formation of large-scale inhomogeneous structures in a spatial distribution of particles due to the -effect: = u_p ( · u_p), where u _p is the random velocity field of the particles which they acquire in a turbulent fluid velocity field. The effect is caused by inertia of particles which results in divergent velocity field of the particles. This results in additional turbulent nondiffusive flux of particles. The mean-field dynamics of inertial particles are studied by considering the stability of the equilibrium solution of the derived evolution equation for the mean number density of the particles in the limit of large Péclet numbers. The resulting equation is reduced to an eigenvalue problem for a Schrödinger equation with a variable mass, and a modified Rayleigh-Ritz variational method is used to estimate the lowest eigenvalue (corresponding to the growth rate of the instability). This estimate is in good agreement with obtained numerical solution of the Schrödinger equation. Similar effects arise during turbulent transport of gaseous admixtures (or light noninertial particles) in a low-Mach-number compressible fluid flow. The discussed effects are important in planetary and atmospheric physics (cloud formation, pollutant dynamics, preferential concentration of particles in protoplanetary disks and also planetesimals in them).     

Integral Equations for Kinematic Dynamo Models

A new technique for the treatment of the kinematic dynamo problem is presented. The method is applicable when the dynamo is surrounded by a medium of finite conductivity and is based on a reformulation of the induction equation and boundary conditions at infinity into an integral equation. We show that the integral operator involved here is compact in the case of homogeneous conductivity, which is important for both mathematical and numerical treatment. A lower bound for the norm of then yields a necessary condition for the generation of magnetic fields by kinematic dynamos. Numerical results are presented for some simple ²-dynamo models. The far-field asymptotics for stationary and time-dependent field modes are discussed.     

Die anlagerungsgechwindigkeit der elektrisch geladenen und neutralen Emanationsfolgeprodukte an das atmosphärische Aerosol

Zusammenfassung Die Anlagerungsgeschwindigkeiten der elektrisch geladenen und neutralen²¹²Pb (ThB)-Atome an das atmosphärische Aerosol wurden experimentell bestimmt. Bei einer mittleren Aerosolkonzentration von 5·10⁴ Teilchen/cm³ wurden die Anlagerungshalbwertszeiten _a = 29 für positive und _a ⁰ = 46 für neutrale Radon-Folgeprodukte erhalten. Ausserdem konnte gezeigt werden, dass bis zu 40% der Teilchen des atmosphärischen Aerosols dem RadienbereichR10^–6cm angehören, und dass dieser Teilchenanteil die Grösse der Anlagerungshalbwertszeiten nur geringfügig (2–4%) beeinflusst, d.h. der Anteil der angelagerten Radionuklide ist in diesem Teilchenradienbereich vernachlässigbar. Zum Schluss wurde mit Hilfe der gemessenen Anlagerungskonstanten der prozentuale Anteil der unangelagerten²²²Rn- und²²⁰Rn-Folgeprodukte in der Atmosphäre berechnet.

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Summary The velocities of attachment of neutral and charged radon-220 daughters to the natural atmospheric aerosol were measured. The half-lives of attachment _a = 29 for positive and _a ⁰ = 46 for neutral radon decay peoducts were found with an average aerosol concentration of 5·10⁴ particles/cm³. It is also shown that about 40% of the atmospheric particles have radiiR10^–6 cm and that these particles have only a small influence (2–4%) on the values of the half-lives of attachment; therefore, in this range of particle radii the number of the attached radioactive atoms can be neglected. Finally the percentage of the unattached²²²Rn and²²⁰Rn-decay products in the atmosphere was computed.

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Résumé Les vitesses de l'agglomération des descendats neutres et électriquement chargés de²²⁰Rn atomes à l'aérosol atmosphérique sont mésurées. Les périodes de l'agglomération _a = 29 pour les descendants positives et _a ⁰ = 46 pour le neutres, étaient établis à une concentration d'aérosol moyenne de 5·10⁴ particules/cm³. De plus on pouvait montrer, que jusqu'à 40% des particules de l'aérosol atmosphérique ont un rayonR10^–6cm et que cette part des particules n'a que une petite influence sur la valeur des périodes d'agglomération (2–4%), c'est-à-dire que le nombre des descendants agglomérés à cet domaine des rayons est négligeable. Finalement le pourcentage des particules non-agglomérés a eté calculé au moyen des paramètres de l'agglomération mésurées.

     

Recent developments in photochemistry of atmospheric ozone

Summary A review is given of the increasingly rapid development of the photochemistry of odd oxygen particles which has taken place since the validity of the classical (oxygen only) theory was for the first time questioned by Hampson and Hunt less than 10 years ago. The relative importance of different reactions is discussed as a function of altitude and also the alterations of the H-system, introduced by NO_x, are investigated. It is shown that the fact that not only the observed ozone but also the HNO₃ distribution should be explained considerably limits the acceptable values of poorly known rate constants. The influence of stratospheric pollution on ozone concentration is also discussed under the assumption of photochemical equilibrium.List of symbols Õ Odd oxygen particles - active hydrogen particles - O^* excited (¹ D)-O-atom - NO_x nitrogen oxides (odd nitrogen) - n ₁ concentration of atomic oxygen [particles cm^–3] - n ₁ ^* concentration of excited [¹ D]-oxygen-atoms - n ₂ concentration of molecular oxygen - n _m concentration of air molecules - s =n _m /n ₂ - ñ n ₁+n ^*+n ₃, concentration of odd oxygen particles - x concentration of atomic hydrogen - y concentration of OH-radicals - z concentration of HO₂-radicals - [NO] concentration of nitric oxide - [NO₂] concentration of nitrogen dioxide - [NO₃] concentration of nitrogen trioxide - [NO_x] concentration of total odd nitrogen - [HNO₃] concentration of nitric acid - k _i reaction rates - f _i dissociation rates - a ₃ fraction off ₃ yielding excited O-atoms - [nomix] NO _x /air mixing ratio - relaxation time Part of the research reported in this article was done at the National Center for Atmospheric Research, Boulder, Colo. (sponsored by the National Science Foundation). The opportunity of using NCAR's computing facilities is especially acknowledged. This study has also been supported by the Swiss National Foundation.     

The partitioning of Triclosan between aqueous and particulate bound phases in the Hudson River Estuary

The distribution of Triclosan within the Hudson River Estuary can be explained by a balance among the overall effluent inputs from municipal sewage treatment facilities, dilution of Triclosan concentrations in the water column with freshwater and seawater inputs, removal of Triclosan from the water column by adsorption to particles, and loss to photodegradation. This study shows that an average water column concentration of 3 ± 2 ng/l (in the lower Hudson River Estuary) is consistent with an estimate for dilution of average wastewater concentrations with seawater and calculated rates of adsorption of Triclosan to particles. An average Triclosan sediment concentration of 26 ± 11 ng/g would be in equilibrium with the overlying water column if Triclosan has a particle-to-water partitioning coefficient of k_d  10⁴, consistent with laboratory estimates.     

Traces of NO 3 ′ ions contained in ice crystals influence charge separation upon crystal fragmentation

Summary If needle-shaped ice crystals are grown in an atmosphere containing traces of nitrous gases, the amount of electrical charge generated when sharp crystal points break away, is between 10 and 50 times as high as in the case of crystals grown in absence of nitrous gases A definite relation has been found to exist between the NO ₃ ion concentration of the ice crytals and the amount of charge (average value 2.7×10^–8, maximum value 13×10^–8 coulombs per gram of ice splinters) generated upon fragmentation. The relation found is possibly of importance with respect to thunderstorm electricity generation.Physikalisch-Bioklimatische Forschungsstelle der Fraunhofer-Gesellschaft, Garmisch-Partenkirchen.     

Humidity effects on gravitational settling and Brownian diffusion of atmospheric aerosol particles

The dependency on relative humidity of the settling velocity of aerosol particles in stagnant air and of the diffusion coefficient due to Brownian motion of aerosol particles was computed for six aerosol types and different particles sizes in dry state. The computations are based (1) on mean bulk densities of dry aerosol particles obtained from measurements or from the knowledge of the chemical composition of the particles, (2) on micro-balance measurements of the water uptake per unit mass of dry aerosol substance versus water activity at thermodynamic equilibrium, and (3) on measurements of the equilibrium water activity of aqueous sea salt solutions. The results show a significant dependence of the settling velocity and Brownian diffusion of aerosol particles on relative humidity and on the particle's chemical composition.Nomenclature A surface parameter of a particle - B surface parameter of a particle - c _L velocity of sound in moist air - C 1+Kn[A+Qexp(–B/Kn]=slip correction - D diffusion coefficient of a particle - D ₁ D(=1)=diffusion coefficient of a spherical particle - f P _w /P _we (T,P)=relative humidity (f=0 dry air,f=1 saturated air) - g acceleration due to gravity - g |g| - k 1.3804×10^–16 erg/°K=Boltzmann constant - Kn _L /r=Knudsen number of a particle - Kn _{0 0L} /r ₀=Knudsen number of a dry particle - m 4r ³/3=mass of a particle - m _L 4r ³ _L /3=mass of the moist air displaced by a particle - M mobility of a particle - M ₀ molar mass of dry air - M _w molar mass of water - Ma |u–u _L |/c _L =Mach number of the particles motion relative to the ambient air - n particle number per unit volume of air - P P ₀+P _w =pressure of the moist air - P ₀ partial pressure of the dry air - P _w partial pressure of the water vapour - P _we P _we (T,P)=equilibrium partial water vapour pressure over a plane surface of water saturated with air - Q surface parameter of a particle - r equivalent radius of a particle (radius of a sphere with the particles volume) - r ₀ equivalent radius of a particle in dry state - R 1+0.13Re ^0.85=inertia correction - R ₀ specific gas constant of dry air - R _w specific gas constant of water - Re 2r _L u–u _L / _L =Reynolds number of the particles motion relative to the ambient air - t time - T absolute temperature - u velocity of a particle - u (amount of the) settling velocity of a particle in stagnant air - u ₁ u(=1)=(amount of the) settling velocity of a spherical particle in stagnant air - u _L velocity of the ambient moist air (far enough from the particle where the flow pattern remains undistorted) - W drag coefficient of a particles equivalent sphere - empirical parameter in equation (3.1) - dynamic viscosity of a particles liquid cover - _L dynamic viscosity of moist air - _0L dynamic viscosity of dry air (at the same pressure and temperature like the moist air) - celsius temperature - dynamic shape factor of a particle (=1 for a sphere) - ₀ dynamic shape factor of a dry particle - _L mean free path of the molecules in moist air - _0L mean free path of the molecules in dry air (at the same pressure and temperature like the moist air) - _Po mean free path of the molecules in dry air at the pressureP ₀ of the dry air and the temperature given - factor of solid to liquid change-over (=1 for a solid particle) - mean bulk density of a particle - _L density of the moist air - _0L density of the dry air at the same pressure and temperature like the moist air - ₀ mean bulk density of a dry particle - ₀ mean diameter of the molecules of dry air - _w diameter of water molecules - relaxation time of a particle - gradient operation - 3.141593     

Effects of geomagnetic activity on the mesospheric electric fields

The results of three series of rocket measurements of mesospheric electric fields carried out under different geomagnetic conditions at polar and high middle latitudes are analysed. The measurements show a clear dependence of the vertical electric fields on geomagnetic activity at polar and high middle latitudes. The vertical electric fields in the lower mesosphere increase with the increase of geomagnetic indexes K_p and K_p. The simultaneous increase of the vertical electric field strength and ion conductivity was observed in the mesosphere during geomagnetic disturbances. This striking phenomenon was displayed most clearly during the solar proton events of October, 1989 accompanied by very strong geomagnetic storm (K_p = 8+). A possible mechanism of generation of the vertical electric fields in the mesosphere caused by gravitational sedimentation of charged aerosol particles is discussed. Simultaneous existence in the mesosphere of both the negative and positive multiply charged aerosol particles of different sizes is assumed for explanation of the observed V/m vertical electric fields and their behaviour under geomagnetically disturbed conditions.Paper Presented at the Second IAGA/ICMA (IAMAS) Workshop on Solar Activity Forcing of the Middle Atmosphere, Prague, August 1997     

Relation between concentrations of giant chloride nuclei and exchange in the atmosphere

Summary In Northern Bohemia 33 research flights were made during which concentration of giant condensation chloride nuclei was measured up to a height of 3,500 m above the earth's surface. Chloride particles were determined by traces left by them in a sheet of gelatine with silver nitrate (Liesegang circles). The actual size of the particles was obtained by comparison of particles of a known size, falling in a sedimentation tube, with images in the sensitive sheet, and the result was adapted to the analysis of samples during the flight. For each level at which a sample was exposed the spectrum of the sizes of nuclei was determined. During the year the average concentration of the giant chloride nuclei at a height of 100 m above the earth was 7.3×10^–3 cm^–3. At greater heights concentration of the nuclei decreased successively, so that at 2,000 m it was only 0.3×10^–3 cm^–3 and above the level of 3,000 m the nuclei occurred sporadically, on the whole. Under the influence of atmospheric exchange the concentration of the nuclei in the boundary layer up to 1,000 m above the earth's surface changes considerably both during the day and during the year. The highest concentration occurs at a height of several hundred metres above the earth in the winter month, at the morning and evening hours, i.e. during a more stable temperature lapse rate. From the established concentrations of the nuclei relation between the turbulent diffusion coefficient and the height above the earth was determined. Its average value during the year increases up to a height of 300 to 400 m above the earth. Above this level it decreases roughly according to the relation ofKz ^–6/7. The exponent changes not only with temperature stratification (with the time of day and year), but also with the average wind speed. For sodium-chloride particles of 2.5 in diameter the maximum value of turbulent diffusion coefficient (at level of 400 m), reaches about 18×10³ cm² sec^–1 while the minimum value is about 5×10³ cm² sec^–1 (above 2,000 m).     

Spontane Bildung negativer Raumladungen in einem maritimpolaren Luftkörper mit hoher Aerosolkonzentration

Zusammenfassung In einem maritim-tropischen Luftkörper wurde während mehrerer Tage beobachtet, dass sich in 50–200 m über dem Boden spontan negative Raumladungen ausbilden, wenn kalte Hangabwinde in die bodennahe Luftschicht eindringen und sich mit der vorher vorhanden gewesenen erwärmten Luft turbulent vermischen. Der «luftelektrisch aktivierbare» Luftkörper zeichnete sich durch extrem hohe Aerosolkonzentration aus. Das Partikelspektrum war in Richtung auf grobe Aerosolkomponenten verschoben.

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Summary Spontaneous formation of negative space charges 50–200 m above the ground has been observed for several consecutive days in a warm maritime (mT) air mass penetrated by cold mountain-slope winds; the cold air underwent turbulent mixing with the pre-existing warm air. The electrifiable airspace was characterized by an extremely high aerosol concentration, with the size distribution spectrum shifted from the normal toward a significantly increased incidence of coarse particles.

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Physikalisch-Bioklimatische ForschungsstelleGarmisch-Partenkirchen der Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung.     

Comparison of model electron densities and temperatures with Millstone Hill observations during undisturbed periods and the geomagnetic storms of 16–23 March and 6–12 April 1990

Measurements of F-region electron density and temperature at Millstone Hill are compared with results from the IZMIRAN time-dependent mathematical model of the Earths ionosphere and plasmasphere during the periods 16–23 March and 6–12 April 1990. Each of these two periods included geomagnetically quiet intervals followed by major storms. Satisfactory agreement between the model and the data is obtained during the quiet intervals, provided that the recombination rate of O⁺(⁴S) ions was decreased by a factor of 1.5 at all altitudes during the nighttime periods 17–18 March, 19–20 March, 6–8 April and 8–9 April in order to increase the NmF2 at night better to match observations. Good model/data agreement is also obtained during the storm periods when vibrationally excited N₂ brings about factor-of-2-4 reductions in daytime NmF2. Model calculations are carried out using different expressions for the O⁺ – O collision frequency for momentum transfer, and the best agreement between the electron-density measurements and the model results is obtained when the CEDAR interim standard formula for the O⁺ – O collision frequency is used. Deviations from the Boltzmann distribution for the first five vibrational levels of NI were calculated. The calculated distribution is highly non-Boltzmann at vibrational levels j > 2, and the Boltzmann distribution assumption results in the increase of 10–30% in calculated NmF2 during the storm-time periods. During the March storm at solar maximum the model results obtained using the EUVAC solar flux model agree a little better with the observations in comparison with the EUV94 solar flux model. For the April storm period of moderate solar activity the EUV94X model results agree better with the observations in comparison to the EUVAC model.     

Measurements of the coefficient of combination of small ions with aerosol particles

Summary The equilibrium small ion concentration (n) was measured in aerosols for various ionization rates (q) and particle concentrations (Z). The results agree with the formulaq=bZn+n ². These experiments were carried out with different particle sizes and the results provided a series of values of the combination coefficientb. The size of the particles was determined by the diffusion box method and the diameter (d) ranged from 0.01 to 0.1 microns. The results fitted an empirical formulab=0.29d.     

On the efficiency with which aerosol particles of radius larger than 0.1 μm are collected by simple ice crystal plates

A theoretical model is presented which allows computing the efficiency with which aerosol particles of radius 0.1r10 m are collected by simple ice crystal plates of radius 50a _c 640 m in air of various relative humidities, temperatures and pressures. Particle capture due to thermophoresis, diffusiophoresis and inertial impaction are considered. It is shown that the capture efficiency of an ice crystal in considerably affected by phoretic effects in the range 0.1r1 m. For aerosol particles ofr>1 m the efficiency is strongly controlled by the flow field around the crystal and the density of the aerosol material. Trajectory analysis also predicts that aerosol particles are preferentially captured by the ice crystal rim. Our theoretica results are found to agree satisfactorily with the laboratory studies presently available. Comparison shows that for the same pressure, temperature and relative humidity of the ambient air ice crystal plates are better aerosol particle scavengers than water drops.     

Chemical aspects of iron oxide coagulation in water: Laboratory studies and implications for natural systems

Initial coagulation rates of colloidal hematite (-Fe₂O₃) particles (diameter less than 0.1 µm) were measured experimentally in well-defined laboratory systems at constant temperature. The relative stability ratio,W, was obtained at various ionic strengths in NaCl medium and at pH values in the range from 3 to 12. ExperimentalW values ranged from 1 to 10⁴ in various systems. The results delineate the roles ofspecific andgeneralized coagulation mechanisms for iron oxides. Among the specifically-interacting species (G _ads ⁰ >G _coul ⁰ ) studied were phosphate, monomeric organic acids of various structures, and polymeric organic acids. The critical coagulation-restabilization concentrations of specifically-interacting anions (from 10^–7 to 10^–4 molar) can be compared with the general effects of non-specific electrolyte coagulants (10^–3 to 10^–1 molar). The laboratory results are interpreted with the help of a Surface Complex Formation/Diffuse Layer Model (SCF/DLM) which describes variations of interfacial charge and potential resulting from variations of coagulating species in solution. Comparison of these laboratory experiments with observations on iron behavior in estuarine and lake waters aids in understanding iron removal mechanisms and coagulation time scales in natural systems.     

Explosive source and its influence on ground motion dynamics

Summary In adjusting measured values in sets A(r*), v(r*) and f(r*) by means of a power function in the form of P=Kr^* a region of discontinuity of the approximating curves was found at the distance r*11.5 m kg ^–1/3. It is assumed that this discontinuity was caused by the varying character of the source of seismic waves. For scaled distances r*>11.5 m kg ^–1/3 the explosion was considered to be a spherical source from the point of view of the charge geometry and of the distance of the pick-up from the centre of the charge, whereas if r*<11.5 m kg ^–1/3 the explosion in the borehole had the character of a cylindrical source. The difference of the two types of sources was reflected in the exponent with both the functions A(r*) and v(r*), so that for r*>11.5 m kg ^–1/3 –4.0 and–2.4, and for r*<11.5 m kg ^–1/3 –2.5 and–1.5. For the same intervals of scaled distance in the set f(r*)1.4 and1.2.     

Distribution of empirical recurrence intervals for segment-rupturing earthquakes on active faults of the Chinese mainland

IntroductionInassessingtheprobabilitiesoftime-dependentandlong-termseismichazardsforsegmentsofactivefaults,itisnecessarytohavetheprobabilitydensity,f(O,fordescribingtherecurrenceintervaldistributionforsegment-rupturingearthquakes.Fromf(nandthefollowingequation,theconditionalprobability,pc,whichincreaseswiththetime,Te,elapsedsincethelatestearthquake,isabletobecalculated(Nishenko,Buland,1987,WorkingGrouponCaliforniaEarthquakeProbabilities,1995;Wen,1995,1998)fwhereATisthetimeintervalforthefor…