Cloud data from the International Satellite Cloud Climatology Project (ISCCP) database have been introduced into the global circuit model developed by Tinsley and Zhou. Using the cloud-top pressure data and cloud type information, the authors have estimated the cloud thickness for each type of cloud. A treatment of the ion pair concentration in the cloud layer that depends on the radii and concentration of the cloud droplets is used to evaluate the reduction of conductivity in the cloud layer. The conductivities within typical clouds are found to be in the range of 2%–5% of that of cloud-free air at the same altitude, for the range of altitudes for typical low clouds to typical high clouds. The global circuit model was used to determine the increase in columnar resistance of each grid element location for various months in years of high and low volcanic and solar activity, taking into account the observed fractional cloud cover for different cloud types and thickness in each location. For a single 5° × 5° grid element in the Indian Ocean, for example, with the observed fractional cloud cover amounts for low, middle, and high clouds each near 20%, the ionosphere-to-surface column resistance increased by about 10%. (For 100%, fraction—that is, uniformly overcast conditions—for each of the cloud types, the increase depends on the cloud height and thickness and is about a factor of 10 for each of the lower-level clouds in this example and a factor of 2 for the cirrus cloud.) It was found that treating clouds, in the fraction of each grid element in which they were present, as having zero conductivity made very little difference to the results. The increase in global total resistance for the global ensemble of columns in the ionosphere–earth return path in the global circuit was about 10%, applicable to the several solar and volcanic activity conditions, but this is probably an upper limit, in light of the unavailability of data on subkilometer breaks in cloud cover.
The global atmosphere electric circuit has been postulated, on the basis of a number of sets of correlations, to play a key role in one of the mechanisms by which solar activity affects the earth climate (Tinsley 2000; Tinsley and Yu 2004; Tinsley 2008; Burns et al. 2008). The most important parameter of the global circuit in this mechanism is the ionosphere–surface current density Jz, which varies with changes of the external drivers (space weather); the internal drivers (current output from thunderstorms and other highly electrified clouds); and the distribution of ionosphere–surface column resistance (which depends on ion production from cosmic rays and other energetic particles from the space environment, as well as ionization losses on natural and anthropogenic aerosols). Effects of Jz on cloud microphysics arise because Jz generates space charge in conductivity gradients because of droplet concentration gradients as it passes through clouds, and the space charge puts charges on the order of 10 to 100 elementary charges on aerosol particles and droplets in these gradients (Zhou and Tinsley 2007; Beard et al. 2004). These charges then change the electrically induced scavenging rates in the regions of space charge by up to an order of magnitude (Tinsley et al. 2000, 2001, 2006; Zhou et al. 2009).
The charges can enhance contact ice nucleation rates by increasing the scavenging of relatively large ice-forming nuclei by supercooled droplets, as modeled by Tinsley et al. (2000). Additionally, the charges can increase the scavenging of the large cloud condensation nuclei (CCN) and decrease the phoretic and Brownian scavenging of the smallest CCN (Tinsley 2004; Zhou et al. 2009). Taken with the correlations noted above, which are for meteorological parameters with Jz or proxies for it, the theory and modeling suggests that these electrical enhancements of cloud microphysical processes can account for the observed small changes in regional cloud cover, precipitation, and atmospheric dynamics. The variations of Jz may cause effects on weather and climate from day-to-day time scales up to Milankovich time scales, and observations and theory have been reviewed by Tinsley (2000), Tinsley and Yu (2004), and Tinsley and Zhou (2006).
While effects of Jz on aerosol scavenging affecting their concentration appear to be small compared to other sources of variability in aerosols, the sustained responses to external drivers and to thunderstorm activity changes responding to climate change may be more important. Thus, it is desirable to include in a global circuit model as many as possible of the atmospheric variables that influence Jz. Clouds can affect Jz locally and globally, in addition to Jz having effects on clouds. The conductivity of the air in the cloud layer is reduced because of the attachment of the small air ions to droplets. A small air ion itself is produced by attachment, within a fraction of a second, of several polar molecules to a charged nitrogen or oxygen molecular ion produced by ionizing radiation. Large air ions are produced when the small air ions, in minutes to hours, become large air ions by attachment to aerosol particles. Here we refer to large air ions as charged aerosol particles, in light of the continual interchange between charged and neutral aerosol particles that is implicit in our model.
Measurements and computations (Pruppacher and Klett 1997, section 18.3.2) show that the conductivity in the cloud could be 1/40 to ⅓ of that of the air outside the cloud because of the attachment of small ions to water droplets. The reduction in conductivity increases the columnar resistance R at that location, which reduces Jz there. With clouds over much of the globe increasing the total resistance to the global circuit return current, there can be an increase in ionospheric potential and an increase in Jz in cloud-free areas compared to a totally cloud-free situation. This Jz increase assumes a constant current output of the thunderstorms and highly electrified clouds that are the main generators of the global circuit. A recent discussion of the variability and relative contributions of such generators in different parts of the globe is given by Kartalev et al. (2006).
Since the 1970s, several global circuit models have been constructed, among them those of Hays and Roble (1979), Roble and Hays (1979), Makino and Ogawa (1985), and Sapkota and Varshneya (1990), with the latter two including simple treatments of atmospheric aerosols. In recent work, Tinsley and Zhou (2006) constructed a global circuit model with more accurate treatments of the effects of solar modulation of the cosmic ray flux on the latitude distribution of internal conductivity and the distributions of aerosol in the free troposphere and planetary boundary layer and their seasonal changes, and they made a simple estimate of the effect of ultrafine aerosol production in the stratosphere at high latitudes. The stratospheric ultrafine aerosol particles are formed from H2SO4 vapor resulting from volcanic eruptions, which condenses in the downward branches of the Brewer–Dobson (Garcia and Solomon 1983) circulation. Changes in the cosmic ray flux over a solar cycle were found to affect the global ionosphere-to-surface return path resistance RT by about 7% and changes in stratospheric volcanic aerosols by about 20%. The regional changes were largest at high latitudes, by up to 20% for the solar cycle effect without aerosols, and up to at least a factor of 3 for stratospheric volcanic aerosol effects. Changes in aerosol distributions from July to December increased RT by about 5%.
It is of interest to know if clouds have effects comparable to those of the solar cycle and aerosols. Here, we introduce the cloud cover data from the International Satellite Cloud Climate Project (ISCCP) database into the global circuit model constructed by Tinsley and Zhou (2006) to show the effect on the local column resistances and the global return path resistance of introducing clouds. We also evaluate, for comparison, the effect on the global resistance of introducing aerosols into an aerosol-free atmosphere.
2. Description of global circuit model
Figure 1 is a schematic circuit diagram representing a half section in the magnetic meridian that includes the dawn–dusk local time plane. The geometry of the global circuit can be treated as plane-parallel because of the large radius of the earth compared to the thickness of the atmosphere. In the model the bottom “plane” is the ground surface, which is equipotential all over the world, and the top plane is the ionosphere effectively at an altitude of 60 km with high conductivity that causes it to be equipotential at latitudes equatorward of about ±60° geomagnetic (gm) latitude. This excludes the geomagnetic polar caps since in the ionospheres of these regions there are additional potential distributions superimposed on the lower-latitude equipotential value due to the interaction among the solar wind, magnetosphere, and ionosphere. The two planes are linked by columns of air that can be treated as independent conductors. The highly electrified convective clouds in three tropical “chimney” regions, the Americas, Africa, and Indonesia–Australia (Williams and Heckman 1993), and in frontal systems and shower clouds at higher latitudes generate upward currents that maintain the potential difference between the ionosphere and the surface. Away from the generator regions the current flows down from the ionosphere to surface, with a current density Jz, which varies with changes of the regional columnar resistance R between ionosphere and surface. The variations of R are due to the effects of geomagnetic latitude on ionizing radiation, as well as to regional changes in the surface altitude, aerosol content and clouds. The circuit diagram in Fig. 1 shows discrete column resistances at equatorial (E), low (L), high (H), and polar (P) latitudes. (The column resistances represent the continuum of conductivity in the conducting atmosphere). In each case a stratospheric columnar resistance S is shown in series with a tropospheric columnar resistance T, although there is no sharp boundary, and there is a continuous variation of conductivity σ(z) over the whole altitude range. Then the total columnar resistance R between the 60-km upper boundary and the surface is given by
where Zs is the elevation of the surface. The current density Jz throughout the column is
where Vi is the overhead ionospheric potential (relative to the potential of the surface, whether ocean or land).
The ion pair concentration and mobility, both increasing with height, determine the columnar resistance. The ion pair concentration nf for the steady condition of fair weather (with no cloud) is obtained by the equation
where q is the ion pair production rate, α is the ion–ion recombination coefficient, and βj is the effective attachment coefficient for j-type aerosol with concentration Sj. The ion–ion recombination (second term) is for small air ions. The summation in the third term includes the attachment of both positive and negative small air ions with neutral aerosol particles and the recombination of both positive and negative small ions with negatively and positively charged aerosol particles (large air ions). At equilibrium the rate of attachment of small ions, as they become charged aerosol particles, is equal to the rate of recombination of the charged aerosol particles with the oppositely charged small ions, and the concentrations become approximately one-third negatively charged aerosol particles, one-third positively charged aerosol particles, and one-third neutral aerosol particles. The effective attachment coefficients are calculated according to the size distribution of the aerosol with the formula suggested by Hoppel (1985) and the extended formula by Tinsley and Zhou [2006, their Eqs. (7) and (8)], who showed (their Fig. 8) that the loss of ions by attachment to aerosol particles exceeded the loss by ion–ion recombination in the planetary boundary layer (except over Antarctica) but not in the free troposphere.
As described by Pruppacher and Klett [1997, section 18.3.2, Eqs. (18)–(37)], who neglected ion–ion recombination and ion attachment to the aerosol, in the weakly electrified cloud in the steady state the ionization rate q is balanced by the loss of ion to droplets at the rate 4πDΣiNiAinc, where D is the ion diffusivity, Ni is the concentration of the cloud droplets with the radius of Ai, and nc is the ion pair concentration in the cloud.
Including this term for ion loss to droplets, the ion pair concentration in the cloud layer in the steady condition, nc, can be obtained by the equation
The ion diffusivity D depends on the ion electrical mobility μ as given by the Einstein formula
where e is the elementary charge, μ/e is the analog of the conventional particle mobility, and the value of μ is dependent on the ion mass. For atmospheric small ions that incorporate clusters of polar molecules, the positive and negative ion mobilities μ1 and μ2 vary according to their total ion masses, which are likely to increase with increasing humidity as the clusters grow with added water molecules (Fujioka et al. 1983). The aerosol concentration will decrease in the cloud as the aerosol particles become attached to droplets. The reduction in mobility due to humidity and an effect of the reduction of aerosol concentration increasing the ion concentration (Zhou and Tinsley 2007) tend to cancel each other. In this work we assume the mobility, aerosol concentration, and ion recombination and attachment rate coefficients in the cloud are as same as that for the cloud-free air at the same level.
We use the variation of mobility with height discussed by Zhou and Tinsley (2007), such that
where μz, pz, and Tz are the mobility, pressure, and temperature at a height z, respectively; and μ0, p0, and T0 are the mobility, pressure, and temperature, respectively, at a reference atmospheric pressure and temperature. Values for μz at several heights are given by Zhou and Tinsley (2007).
As in the model made by Tinsley and Zhou (2006), the tropospheric aerosol concentration and size distribution are from the Global Aerosol Dataset (GADS; Hess et al. 1998) and the stratospheric aerosol concentration and size distribution are derived from the simulation made by Yu and Turco (2001). The conductivity for fair weather and within cloud layers can be obtained by the equation
where σ represents σf , the conductivity for fair weather (with no cloud), or σc, the conductivity in the cloud layer; and n represents nf or nc.
We use the global cloud coverage amount and type data from the International Satellite Cloud Climatology Project D2 database (ISCCP 2004) in which the clouds are divided into three main types (see Fig. 2): low cloud, where the cloud-top pressure is greater than 680 mb, including cumulus, stratocumulus, and stratus; middle cloud, where cloud-top pressure is between 680 and 440 mb, including altocumulus, altostratus, and nimbostratus; and high cloud, with cloud-top pressure between 440 and 50 mb, including cirrus, cirrostratus, and deep convective. The ISCCP D2 dataset is described by Rossow and Schiffer (1999). Deep convective clouds are considered to be the thunderstorm clouds, the generators of the global circuit, and are not included in our model of the resistance of the return path as they occupy only about 2.6% of the globe (Rossow and Schiffer 1999). The fractional coverage of high, middle, and low clouds is highly variable over the globe (this will be illustrated later in Figs. 5a–c and Table 2).
A limitation of the cloud dataset is that there are no entries for cloud cover for night conditions. Thus, there is an absence of entries for high latitudes in the local winters, and the monthly averages of the available data over the rest of the globe are based on daylight conditions. Another limitation of the dataset is that if any cloud is detected in the input data, which has pixel size 4–7 km, it is assumed to fill the whole pixel (Rossow and Schiffer 1999). So clouds which are broken on smaller scales, or which have smaller-scale clear lanes due to downwelling, are treated as being continuous. Preferential flow of electric current density through these small cloud-free (or thin cloud) areas occurs, and there is horizontal spread of current both below and above such breaks in cloud, so that the overall column resistance is overestimated. Another limitation discussed later is in the approximate treatment of cloud-base heights.
The results will show that cloud effects on the global resistance are small compared to aerosol effects; until greater accuracy is available for evaluating aerosol effects and their variability, it is not considered worthwhile to seek greater accuracy in accounting for cloud effects.
Because in general the observations show only partial cloud cover in each 5° × 5° latitude and longitude bin, the equivalent resistivity for each vertical cell of each latitude–longitude bin, r(z), is calculated by the equation
where fx is the fraction of x type cloud in the bin from the ISCCP data, σcx(z) is the conductivity for each x type of cloud, and σf (z) is the conductivity for the fair weather air.
Although the code allows up to 14 different cloud types with their fractional amounts (an ice and a liquid component for three types each of low and middle clouds, and two types of high clouds when deep convective clouds are excluded), we combine fractions of liquid and ice clouds for a maximum of three types at a given level, and a total of eight types.
As in Eq. (1), the columnar resistance R is obtained by
where the resistivity r(z) = 1/σ(z), and Δh is the thickness of each vertical cell in the model. The vertical cells are of 50-m height intervals at sea level, increasing to 500 m at 60-km altitude.
The ISCCP data provide the cloud-top pressure; however, cloud-base pressure is not available at present. So we have to estimate the cloud-base pressure to calculate the depth of the cloud. The definition of the cloud-base height for the ISCCP data follows the method recommended by Ridout and Rosmond (1996), using the Navy Operational Global Atmospheric Prediction System (NOGAPS) hybrid sigma-pressure coordinate system with 18 level grids (Simmons et al. 1989; Hogan and Rosmond 1991). The cirrus, altocumulus, and altostratus clouds are assumed to occupy one grid level, which includes the cloud-top pressure. Cirrostratus clouds are assumed to have a base at 440 mb and nimbostratus clouds are assumed to have a base at the level whose pressure is equal to surface pressure minus 200 mb. The low clouds—cumulus, stratocumulus, and stratus—are assumed to have a base at the level which pressure is equal to surface pressure minus 100 mb. If the calculated base level is above the cloud-top level from ISCCP, the cloud occupies one grid level, which includes the cloud-top pressure. A more accurate value for the increment in column resistance would be obtained by using the approach of Williams et al. (2005) for deriving cloud-base height from air and dewpoint temperatures, but data for utilizing this were not available to us. The pressure as a function of height is obtained by the vertical integration of density obtained from the molecular concentration m of the air, with the following expressions fitted to the values at 0, 10, and 20 km in the U.S. Standard Atmosphere (COESA 1976). The molecular concentration m variation as the function of vertical height is as follows:
The cloud droplet size spectral distribution, ns(r), for the low and middle clouds is from Pruppacher and Klett [1997, Eq. (2.3)]:
where B = 2/rmod and A = N*B3/2.
The cloud droplet radius is r; the mode radius is rmod; the concentrations of the droplets N for cumulus, stratus, stratocumulus, nimbostratus, and altostratus are from Carrier et al. (1967). Since there is a lack of drop concentration and mode radius data for altocumulus, we assume that its drop concentration and mode radius are the same as for cumulus. We assume that the ice mode has the same particle concentration and mode radius as the liquid mode. This assumption affects the reduction of conductivity in the layer to the extent that the summation ΣiNiAi [from Eq. (4)] is different for the two modes.
where N is the concentration; I is the water content; a1, a2, b1, and b2 are temperature related factors; f is an I-related factor; and r0 is a constant, representing a break point in the size distribution with the factors and constants and their units all given by Hess et al. (1998).
There are four months (July, December, March, and September) within three years of cloud cover data that are used in the global circuit model. Cloud data of 1989 represent the solar maximum and low volcanic activity conditions; the data of 1992, which is one year after the eruption of Pinatubo (1991), represent the high volcanic activity and intermediate solar activity condition; and data of 1996 represent the solar minimum and low volcanic activity condition. It was found by Tinsley and Zhou (2006) that the larger volcanic aerosol particles in the lower stratosphere, although effective in scattering visible light, had a negligible effect on column resistances. However, the ultrafine aerosol production in the downward branches of the Brewer–Dobson circulation at upper-stratospheric levels at high latitudes may double the column resistance there, with effects lasting for 5 years or so. The solar activity effect was found to reach ∼20% at high latitudes, where the relative change in cosmic ray flux is greatest.
a. The variation of the conductivity in the cloud layer
Figures 3a–f show the vertical conductivity variation as a function of altitude for July 1996 at latitude 12.5°S and longitude 92.5°E (which is over the Indian Ocean, with roughly average amounts of cloud cover), with the solid curve indicating the results for no cloud and the dashed, dashed–dotted, and dotted line indicating the results with clouds, assuming 100% cloud cover for low (Figs. 3a,b, with cumulus and stratocumulus), middle (Figs. 3c–e with altocumulus, altostratus, and nimbostratus) and high clouds (Fig. 3f with cirrus), instead of the actual fractional cloud cover for that location and time. In each cloud layer the conductivity greatly decreases (i.e., in low, middle, and high cloud layers the conductivities are ∼1/60 to ∼1/20 that of the cloud-free air at the same level).
b. The effect of the cloud on the columnar resistance and conductivity
Figure 4 shows the vertical conductivity at the grid point for latitude 12.5°S, longitude 92.5°E, for the measured average fraction of the cloud cover for the month of July 1996, where for low clouds the coverage of cumulus is 15.8% and stratocumulus 9.3%; for middle clouds the coverage of altostratus is 9.4%, nimbostratus 5.1%, and altocumulus 0.4%; and for high clouds the coverage of cirrus is 18.6%. The solid curve is the vertical conductivity without cloud and the dashed curve is the vertical conductivity with cloud. The reason for the much smaller effect with partial cloud cover than with the 100% cloud cover in Fig. 3 is that the effective conductivity of the partial cloud layers is now dominated by the (unchanged) high conductivity of the fraction of the clear air (that in this case more than 74%) that remains between the broken clouds. Because of the partial nature of the cloud cover, the conductivity at the cloud level only decreases between 0.1% to 24.2% with the amount of decrease depending on the fraction of the cloud in the bin.
Figures 5a–c show the amount and thickness of low, middle, and high clouds along longitude 92.5°E in July 1996, which is the solar minimum and low volcanic activity year. Cloud data are only available from about 55°S to 90°N owing to polar darkness conditions at high southern latitudes. The choice of the 92.5°E meridian includes a wide variation of surface height over ocean and mountains from the South Pole to the North Pole, with large increases in aerosol concentration in industrial areas, as quantified by Tinsley and Zhou (2006). The increases in elevation decrease the column resistance, while the increases in aerosol concentration increase it. Figure 5d shows the columnar resistance for the same meridian. The solid line is the result without cloud and the dashed line is the result with cloud.
With the partial cloud cover in the column the columnar resistance increases compared to the results with no cloud. Low cloud has a considerably greater effect on column resistance than high cloud because the lower the level in the atmosphere, the lower the conductivity (higher resistivity) of the clear or cloudy air. As can be inferred from Fig. 3 or 4, at 10 km the conductivity is 10 times its value at 2 km, so that a given cloud (of whatever fraction) that increases the resistance of its level by a given factor makes a 10 times greater increment to the ionosphere–surface column resistance if it is at 2 km compared to the increment it would make at 10 km. By way of comparison with the fractional cloud cover results, an evaluation of the effect of 100% cloud fraction for these clouds showed increases that depended on cloud height, thickness, and type, with a factor of about 5–10 for the middle and low clouds considered separately, and a factor of about 2 for the cirrus clouds. These results are shown in Table 1.
Over the Indian Ocean (e.g., 30°S)—with the largest fraction of low cloud, and also high ΣiNiAi, as in Eq. (4), owing to the high liquid water content from warm humid air there—the amount of columnar resistance increase is larger than at any other location (Fig. 5d). Over Asian land the curve with cloud is only slightly higher than that without cloud.
c. Latitude distribution of cloud parameters
Because there is a large variation of different cloud types with latitude, we show in Table 2 zonal averages of cloud properties in 10°-wide latitude increments, as extracted from the ISCCP D2 dataset. Because of the absence of winter polar night data, we show the monthly averages of daytime cloud cover (%) and cloud-top and cloud-base heights (in km) for summer conditions represented by December in the Southern Hemisphere and July in the Northern Hemisphere, respectively. The relatively small amounts of cloud cover, particularly low cloud cover, at high southern latitudes in summer is partly on account of the high altitude of most of the Antarctic continent, with colder and more stable conditions there inhibiting convection, compared to high northern latitudes.
d. Global maps of column resistance
Figures 6a–c show global maps of calculated column resistance for conditions (a) with aerosols but no cloud, (b) with fractional cloud cover from the ISCCP dataset, and (c) with fractional cloud cover as in (b) but with conductivity within clouds set to zero. The Northern Hemisphere is for July 1996 and the Southern Hemisphere is for December 1996. From Fig. 6a we see that without cloud the high-altitude regions in Antarctica, Greenland, and the Himalayas have about an order of magnitude less column resistance (greater column conductance) than oceanic regions at low latitudes, particularly the Pacific, Atlantic, and Indian Oceans. The arid high-altitude regions, and to a lesser extent the low-humidity continental regions that are free from industrial pollution, are largely responsible for the low global ionosphere–earth resistance. This resistance is the reciprocal of the global sum of column conductances (i.e., it is the reciprocal of the global sum of the reciprocals of the column resistances).
Clouds further increase (decrease) the column resistances (conductances) as shown in Figs. 3 to 5, and we see the effects over the globe by comparison of Fig. 6b with Fig. 6a. The changes are relatively small compared to the column resistances without clouds and can be seen in pixel darkening, mostly in middle and high latitudes, and over continents where substantial amounts of clouds are present and column resistances are smaller. There is little effect of clouds in the high-altitude arid regions, especially Antarctica, where this and the relatively high column conductances (which make an important contribution toward the global resistance) ensure a relatively small change in global resistance due to clouds.
There is very little change between Figs. 6b and 6c; only 15 pixels are darkened. This and the later quantitative value show that show that zero conductivity for clouds is a good approximation, in view of the other approximations for the model mentioned earlier.
e. The variation of global resistance RT due to the cloud cover
Table 3 shows the global atmospheric resistance (RT), with the results in columns from left to right for neither aerosols nor cloud cover, for clouds but no aerosol (except for stratospheric aerosol in the lowest two rows), for aerosol but no clouds, and for both clouds and aerosols, shown for conditions with high and low solar and volcanic activity in various combinations for the months of July and December in 1989, 1992, and 1996. These months and years represent the range of seasonal, solar cycle, and volcanic conditions. The same results for no cloud are also given for varying solar activity and volcanic activity conditions in Tinsley and Zhou (2006). The value of global resistance RT with no cloud or aerosol is 113 Ω for the solar minimum period and 117 Ω for the solar maximum period. The lowest two rows in the last three columns represent the addition of stratospheric aerosols for volcanic conditions.
The presence of the tropospheric aerosols generally increases the global resistance by 60%–75%, and the addition of the estimated stratospheric volcanic aerosols brings this increase up to about 90%. The results in the second and fourth data columns show the effect of clouds; while different cloud cover data were used for each of the six periods, there were no significant differences between the percentage changes in RT going from cloud-free to cloudy conditions. Table 3 shows that 1989 is the solar maximum year with low volcanic activity, when RT with clouds is 207 Ω, which is 8.4% higher than that without the clouds; 1992 is the year after volcanic eruption of Pinatubo (1991) with high ultrafine aerosol in the stratosphere at high latitudes and medium solar activity, when RT with cloud reaches 233 Ω, which is 8.4% higher than without clouds; 1996 is the solar minimum year with low volcanic activity, when RT with cloud is 192 Ω, which is 7.9% higher than without clouds. So the model gives cloud enhancements of the global resistance by about 8% in all cases, even for the seasonal variation. The seasonal variation of RT is mainly due to the seasonal variation of the aerosol concentration.
Table 4 is similar to Table 3 except that instead of summer and winter conditions, the results are now for the equinoxes. The results are essentially the same as in Table 3, with again about an 8% increase in RT due to clouds in all cases, with the major increases due to aerosols. The increased coverage of clouds in the southern polar region has had no noticeable effect.
Table 5 gives results for RT for the two hemispheres separately, and for clouds treated as having zero conductivity as well as realistic conductivity. The realistic conductivities are based on the same cloud data that are averaged in Table 2 and are associated with the maps in Fig. 6 (i.e., for July in the NH and December in the SH). The differences between the RT values for the two hemispheres are mainly due to the greater amount of ocean in the Southern Hemisphere. The effect of clouds (about 10%) is slightly higher than the previous results and can be attributed to more convective clouds in summer than in winter. However, as discussed earlier, the cloud effects represent an upper limit, so 10% can be taken as characterizing that upper limit.
The differences between the results for zero cloud conductivity result and the real conductivity is less than 1%. The (unrealistic) combination of results for the two hemispheres gives RT values of 184 Ω for aerosol and no cloud, 202 Ω for aerosol and cloud with real conductivity, and 203 Ω for aerosol and zero cloud conductivity. The small effect of clouds on the global resistance thus contrasts with the 60%–90% effect of aerosols. Thus, the aerosols have about an order of magnitude greater effect than clouds in increasing RT above the value for an aerosol-free and cloud-free atmosphere.
4. Summary and discussion
In the cloud layers at a given level with high values of the product ΣiNiAi, as discussed above, high rates of attachment of small air ions to the droplets occur, which causes a large decrease of conductivity in the cloud layer. From models produced by Pluvinage (1946, pp. 31 and 160) and Griffiths et al. (1974), which are in good agreement with measurements (Pruppacher and Klett 1997, section 18.3.2), the conductivity in the cloud layer is typically 1/40 to ⅓ the clear air value at the same level. The condition for the ratio of ⅓ (Allee and Phillips 1959) was for thin clouds and/or open area in clouds of moderate density. Our calculations give the result that within clouds the conductivity is 1/60 to 1/20 of the clear air value (for marine stratus to cirrus). In low-altitude clouds the conductivity is lower than Pluvinage’s value. In the Pluvinage model the concentration of the low cloud droplets was assumed to be 100 cm−3, while the droplet concentration in our model is 3 times higher than Pluvinage’s value. Our more realistic concentration causes greater loss of the ions by attachment to the drops, giving the greater reduction in conductivity.
In each 5° × 5° grid bin the “effective” conductivity at a given level is the average of the relatively high conductivity values for cloud-free air with the relatively low conductivity values for the cloudy air, weighted by the clear and cloud fractions in the bin. For example in Fig. 4, with the 25.1% low cloud in the bin, the conductivity decreases to about three-quarters of the clear air value. The reciprocal of the effective conductivity is the effective resistivity, which is the quantity that is summed in height to give the column resistance as in Eq. (8). Over the Indian Ocean, with the largest amount of thick cloud cover at low altitude (marine cumulus and stratocumulus, as in Fig. 5a), the columnar resistance increase is larger than any other place. Over inland Asia at about 50°N the low amount of low cloud cover and thickness, associated with the downwelling Hadley circulation and desert conditions, causes only a very small increase of the columnar resistance.
The effects of middle and high cloud are smaller than that of low cloud. In Fig. 5 between 20° and 40°N along 92.5°E, although there is about 40% of thick high and about 30% of thick middle cloud cover, the difference of the columnar resistance between the no-cloud condition and the cloud condition is very small. Furthermore, as can be seen in Fig. 5d, the absolute variations in column resistance along the meridian in the cloud-free air that are due to the altitude of the surface and to variations in aerosol content (for details, see Tinsley and Zhou 2006) are much greater than the absolute variation in column resistance due to the cloud cover. Thus, the presence of typical aerosol particle concentrations in the troposphere and ultrafine aerosol particles in the stratosphere has a greater effect on the columnar resistance than that of clouds. This is also shown by comparison with the model results for RT with and without aerosols in Tables 3 and 4.
This model with clouds was developed from the initial global circuit model constructed by Tinsley and Zhou (2006). A treatment to deal with the reduction of conductivity in cloud layers is introduced. With typical low to high cloud layers the conductivity is only 2%–5% of that of cloud-free air at the same level. The inclusion of measured fractional cloud amounts with estimated cloud thickness for each cloud layer can increase the columnar resistance at a given location significantly, by as much as 20% for measured 45% fractional cloud low cloud cover (marine stratocumulus and cumulus). The effect of low cloud on columnar resistance is stronger than that for middle and high cloud. This is because the decreasing resistivity of air with altitude means that a given cloud at high altitude contributes less to the column resistance than if it was at low altitude. The global effects of actual fractional cloud cover on the total ionosphere–earth return path resistance are generally to increase that resistance by an upper limit of about 10% as compared to the larger effect of aerosols, mainly in the continental boundary layer, that increase it by about 60%.
We are grateful to Dr. Earle Williams and an anonymous reviewer for their valuable comments, which significantly improved the quality of the manuscript. This work has been funded by Grant ATM-0242827 by the U.S. National Science Foundation. Limin Zhou has been supported in part by grants of the Chinese National Science Foundation (40701195), grants of Chinese National Postdoctoral Foundation (special support: 200801192 and 20070420632) and grants of the Science and Technology Commission of Shanghai Municipality (07XD14010).
Corresponding author address: Dr. Limin Zhou, 3663 North Zhongshan Road, Department of Geography, East China Normal University, Shanghai 200062, China. Email: email@example.com