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ATMOSPHERIC ELECTRICITY IN THE PLANETARY BOUNDARY LAYER 152 charge-exchange, and clustering reactions with the molecular species present in the air. Much progress has recently been achieved in understanding this chain of ionic reactions in well-defined laboratory gases (Huertas et al., 1978) and in the upper atmosphere (Arnold and Ferguson, 1983). In the troposphere, where trace gases are numerous and variable, the ion chemistry is complicated, and the composition of the terminal ion must be regarded as uncertain at best. If mass spectroscopic measurements can be extended to identify ambient ions, it is possible that this identification can be used as a measure of certain elusive trace gases in the troposphere. Fortunately, the ion nature enters the equations that govern atmospheric electricity in the PBL only as it affects the ionic mobility and recombination coefficient. The mobility is defined as the mean drift velocity of the ion per unit electric field. The mobilities of ambient ions are more easily determined than their mass or chemical composition. (There is no unique relationship between mobility and mass, and a rather large uncertainty in mass translates into a much smaller uncertainty in mobility.) Values for aged positive and negative ion mobilities at STP are about 1.15 and 1.25 cm2 Vâ1 secâ1, respectively (Mohnen, 1977), are inversely proportional to air density, and are independent of electric-field strength. If ions are formed in pairs by ionizing radiation and annihilated in pairs by ion-ion recombination, then the positive and negative ion concentrations are equal and, in the absence of particulates, are given by where q is the ionization rate and is the recombination coefficient. If there are no aerosol particles in the atmosphere the ion lifetime is given by Recombination of ions in the troposphere is a three-body process. The present theoretical treatment of three-body recombination is inadequate for calculation of absolute values of the recombination coefficient. This is due in part to our inability to identify the ion chemistry. Measurements of the recombination coefficient yield a value of about 1.4 Ã 10â6 cm3/sec for aged atmospheric ions at STP (Nolan, 1943). The movement of ions in an electric field gives rise to the electrical conductivity of the atmosphere. The conductivity is defined as where kÂ± is the mobility and e is the elementary charge. The conductivity is non-ohmic (field dependent) if the ion densities depend on electric field, as is the case near a boundary (electrode effect). Equations (11.1)-(11.3) predict concentrations of about 3000 ions/cm3, lifetimes of about 5 min, and a conductivity of about 1 Ã 10â13 mho/m for an ionization rate of 10 ion pair cmâ3 secâ1. In reality the values of these variables are considerably smaller because ions are destroyed not only by recombination but also by attachment to aerosol particles, as described in the next section. Attachment of Ions to Aerosol Particles Suspended in the atmosphere are many small particles mostly in the size range between 0.01 to 0.5 Âµm radius. The concentration of aerosol particles varies from a few hundred per cubic centimeter over remote regions of the oceans to a hundred thousand per cubic centimeter in polluted urban environments. Ions diffuse to these particles and, on contact, transfer their charge to them; thus the particles act as centers of recombination. In most continental areas the loss of ions by attachment to aerosol particles is greater than the loss by ion-ion recombination. The attachment process also establishes a size-dependent statistical charge distribution on the aerosol particles. (Some are negatively, some positively, and some neutrally charged.) To treat the problem of ion-aerosol attachment in its totality requires the solution of a system of balance equations for ions and particles with various numbers of elementary charges. Since we are interested here only in the effect of aerosols on ion depletion, we can write a simplified ion balance equation as where Z is the total particle concentration irrespective of the charge state of the individual particles and Î² is the effective ion-aerosol attachment coefficient. For steady-state conditions and q = 10 ion pairs cmâ3 secâ1, the dependence of ion density on the particle concentration is shown in Figure 11.2 for an effective attachment coefficient of Î² = 2 Ã 10â6 cm3 secâ1. It is readily seen that when the particle concentration is greater than about 1000 cmâ3, the concentration of ions is more dependent on the aerosol attachment than on ion-ion recombination. Only in remote oceanic and Arctic regions can the effect of particles on the ion density sometimes be ignored. Atmospheric aerosols are hygroscopic, and their equilibrium radius increases as the relative humidity in