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ATMOSPHERIC ELECTRICITY IN THE PLANETARY BOUNDARY LAYER 153 creases. This growth is especially pronounced at relative humidities above about 90 percent. An increase in the size of aerosol particles makes them more efficient scavengers of ions, resulting in a lower conductivity. When the relative humidity exceeds 100 percent, some of the particles are activated and grow rapidly (by about 2 orders of magnitude) to radii larger than 1 Âµm, forming fog or cloud droplets. These droplets are effective scavengers of ions and are responsible for the low conductivities found in fogs and clouds. The atmospheric-electric fog effect (see section below on Phenomenology of Atmospheric Electricity in the Planetary Boundary Layer), where conductivity decreases and the electric field increases before the formation of fog, is probably related to aerosol growth with increasing humidity. Figure 11.2 Ion depletion as a function of increasing aerosol concentration for an ionization rate of 10 ion pairs cmâ 3 secâ1 and a typical value of ion-aerosol attachment coefficient. Recent advances in aerosol measurements have resulted in accurate aerosol size distributions that could now be used to evaluate more thoroughly the ion-aerosol equilibrium. An accurate treatment would include not only a realistic aerosol size distribution but also the statistics of diffusional charging of particles by ions. Effect of the Global Circuit Electric fields and currents in the PBL arise primarily from the voltage impressed across it by the global circuit discussed in Chapter 15 (this volume). The weak conductivity of the PBL causes it to act as a resistive element in the global circuit, conducting a fair-weather current density of about 1 to 3 pA/m2 to ground where the fair-weather electric field is about 100-200 V/m. Because the PBL is the region of greatest electrical resistance, it largely controls the discharge rate of the global circuit. If the conductivity of the atmosphere were uniform, it would be a passive ohmic medium with no accumulation of space charge to alter the electric field. Space charge is generated internally in the unperturbed atmosphere in two ways: (1) by conduction down a conductivity gradient and (2) by the imbalance of ion flow near a boundary. The first mechanism can be understood in terms of Ohm's law, J = Î»E, where J is the conduction-current density. For steady- state conditions and in the absence of any convective charge transport, J is uniform, and, therefore, the electric field is inversely proportional to the conductivity. Since conductivity changes with altitude, there must be an inverse altitude dependence of the electric field. Poisson's equation requires this change in field to be accompanied by a space charge given by where Îµ0 is the dielectric permeability of air. By the steady-state assumption, the first term on the righthand side vanishes and the space charge is proportional to the electric field and conductivity gradient and inversely proportional to the conductivity. This process can be thought of as a pileup of space charge due to conduction down a conductivity gradient. The second mechanism for producing space charge operates only near a boundary. Across any horizontal area in the atmosphere stressed by a vertical electric field, positive and negative ions will flow in opposite directions. However, at a boundary, ions of one sign can flow to that boundary, but there will be no compensating flow of the opposite sign away from it. This imbalance in ion flow gives rise to a space charge in the vicinity of the boundary. This second mechanism for generating space charge is aptly referred to as the electrode effect. For the case of uniform volume ionization in laminar airflow with no aerosols and bounded on the bottom by a conducting surface, the ion- balance equations can be solved together with Poisson's equation to give the solution shown in Figure 11.3. The ionization rate was taken to be 10 ion pairs cmâ3 secâ1, and the solution illustrates that the effect of the electrode, in this idealized case, would extend to about 3 m (Hoppel, 1967). In the turbulent atmosphere, the electrode effect extends to much higher altitudes and the space charge formed by these two mechanisms is dispersed by turbulent mixing, causing a convective flux of charge in addition to the conduction current.