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July-August 2016

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Weather Queries

How do you know if it is fog or haze here in the mountains of south-central Pennsylvania? I have a terrible time figuring this out.

Rita Atwell-Holler

Clearville, Pennsylvania

This is not an easy question to answer, but I'll try to answer it without regard to your geographic location. There is a narrow range of relative humidity, from slightly less than 100% to slightly more, that marks the transition from haze to fog. Within this narrow range, you won't be able to measure the relative humidity with sufficient precision: the instruments for doing so are just too expensive. So backyard humidity measurements will not suffice to tell you whether the reduction in visibility is due to haze or fog. A more promising way to tell the difference is to note the color of what's suspended in the air. If it's white or gray, it's probably fog. If it's a subtle shade of blue or yellow-brown, it's probably haze. The reason for this is an interesting story.

It's appropriate first to visit the definitions of fog and haze. Fog is just a cloud of water droplets on the ground. The droplet concentration often exceeds 100 cm−3 (per cubic centimeter). Droplet diameters range from roughly 2 μm (micrometer—one millionth of a meter) to 20 μm. The fall speeds of such droplets are so low that the slightest drift of air is sufficient to keep them suspended. By definition, fog reduces visibility to 1 km (kilometer) or less.

Haze consists of particles, solid or liquid, suspended in the air. Natural sources are soil dust, sea salt, smoke from lightning-caused fires, and volcanic ash. Plants, especially trees, are a significant natural source of haze. They emit pollen but also hydrocarbon gases into the atmosphere, which are converted to haze particles. Human-caused sources are those from industry, fossil fuel combustion, and deliberate biomass burning. Haze particles are much smaller than cloud droplets, ranging from less than .05 μm to a few μm in diameter. When haze is thick enough to reduce visibility to a few kilometers, the particle concentration can exceed 10,000 cm−3.

Some haze particles, are wettable, this is, they attract water vapor. The vapor may condense on the particle as a thin film, thereby increasing its size. If, in addition, the particle is soluble in water, such as salt (sodium chloride), the film of condensate dissolves the particle to form a solution droplet. If the solution droplet is growth-limited, it contributes to the haze. I'll have much more to say about this later. Other particles do not attract water vapor and produce a dry haze. For example, particles of pure silica sand are not wettable.

Consider the interface between a surface of liquid water and air. Water molecules are in a constant state of agitation, but they are attracted to each other much more in the liquid phase than in the gaseous phase. Some molecules have enough energy to escape the liquid and move to the air (evaporation). Some water molecules in air have enough energy to cross the interface and become part of the liquid (condensation). An interchange of water molecules in both directions is always occurring at the interface. Whether the liquid gains more water molecules than the air depends upon the difference between the vapor pressure in the air and the vapor pressure at the surface of the liquid. If the vapor pressure in the air is less, then there will be net evaporation of the liquid. If the vapor pressure of the air is greater than the vapor pressure at the surface of the liquid, then there is net condensation. If the two vapor pressures are the same (the equilibrium vapor pressure), then the number of molecules crossing the interface is the same in both directions.

Figure 1.  Four Köhler curves giving the equilibrium saturation ratio for tiny droplets that have salt dissolved in them. The amount of salt dissolved in the droplets is given by the diameter of the salt particle before it dissolved: 0.01, 0.02, 0.03, and 0.04 μm. The horizontal axis gives the diameter of the solution droplet. The vertical axis is essentially the relative humidity without the percent. The horizontal line at 1.00 marks the boundary between subsaturated air (below the line) and supersaturated air (above the line). Equilibrium values lie along each curve. If a droplet of a given diameter and with a given amount of dissolved salt lies on one of these curves, it will neither grow by condensation nor evaporate.

The tiniest water droplets have strictly spherical shapes because the mutual attraction of water molecules minimizes the surface area, forming a sphere. The smaller the sphere, the more neighbors each molecule on the surface of the droplet has. For this reason, the equilibrium vapor pressure for the tiniest droplets is greater than that for larger droplets. The extreme case is a puddle, which presents a flat surface of liquid water. The equilibrium vapor pressure over a puddle of pure water is the basis for the definition of relative humidity. Relative humidity (RH) is the ratio, expressed as a percent, of the actual vapor pressure in the air e to the equilibrium vapor pressure es over a flat surface of liquid water. RH = e/es × 100.

At this point, it should be evident that the vapor pressure in air must exceed es, i.e., the air must be supersaturated, before a tiny droplet of pure water can condense from the air. Moreover, the smaller the droplet, the greater the supersaturation must be. For example, let esr be the equilibrium vapor pressure at the surface of a droplet of radius r and consider the supersaturation ratio esr / es. For a radius of 1 μm, the ratio is 1.001, which is to say that the supersaturation required to keep a 1-μm droplet from evaporating is very slight (.001). For a radius of 0.1 μm, the ratio is 1.01. For a radius of 0.01 μm, the ratio is 1.11, which represents a very large supersaturation, which hardly ever occurs. How, then, can the tiniest droplets form? They must grow from something!

Figure 2.  A single Köhler curve, like those in Fig. 1, but for a salt particle of diameter 0.015 μm dissolved in water. The curve shows the diameter that this solution droplet will have when in equilibrium with its surroundings, given values of the saturation ratio. The dashed horizontal line at a saturation ratio of 1.01 represents a nominal supersaturation of the surroundings. The vertical dash-dot line, which passes through the hump on the Köhler curve, is the dividing line between haze and fog or cloud. The letters A, B, and C are explained in the text.

The answer is a condensation nucleus, a particle upon which water vapor may easily condense. Haze particles best suited to become condensation nuclei are larger than average, wettable, and soluble in water. It is fortunate that many of them are always present, even in clean air. Otherwise clouds and fog would form much less readily. Here's why:

A haze particle like salt is a good condensation nucleus. Not only is it wettable, but it also dissolves in water. Because ions from the dissolved salt take the place of some water molecules on the surface of a droplet, a water molecule at the surface will have less of its kin immediately adjacent, thus reducing the equilibrium vapor pressure at the surface of the droplet substantially.

Figure 1 is from the book Atmospheric Thermodynamics by Craig Bohren and Bruce Albrecht. It is called a Köhler diagram, in this case for salt particles of different diameters: 0.01, 0.02, 0.04, and 0.08 μm. The horizontal axis is the diameter of the solution droplet (the salt particle dissolved in water condensate). The vertical axis is the ratio of vapor pressure at the surface of the solution droplet to es, the equilibrium vapor pressure over a flat surface of pure water, mentioned above. Notice that a salt nucleus of diameter 0.04 μm, dissolved in a droplet of diameter about 0.09 μm, is in equilibrium with its surroundings for a saturation ratio of 0.90, equivalent to a relative humidity of 90%. As we saw earlier, a larger droplet of pure water with diameter 0.2 μm, is in equilibrium with its surroundings for a saturation ratio of 1.01 (RH = 101%). Evidently, solution droplets can form at much lower humidities than pure water droplets, which explains the essential role of condensation nuclei.

Again refer to Figure 1, and assume that the RH in the air is 100% (represented by the solid horizontal line drawn for Saturation Ratio = 1.00). A solution droplet, formed by condensation on a 0.01 μm-diameter salt particle, can grow until it reaches a diameter of about 0.035 μm (the diameter corresponding to the intersection of the curve labeled 0.01 and the line for a saturation ratio of 1.00). At this point of intersection, the droplet is in equilibrium. For this droplet to grow larger, the saturation ratio must exceed 1.00. In fact, this droplet is growth-limited unless the saturation ratio reaches nearly 1.04 (the hump in the curve for 0.01).

Figure 2 is also from the book by Bohren and Albrecht. It helps to clarify the point that growth of a solution droplet in a subsaturated environment (RH < 100%) is strictly limited. Here, there is only one Köhler curve, for a salt particle of diameter 0.015 μm. If a droplet in equilibrium at Point A is suddenly placed in an environment where the saturation ratio is given by the horizontal dotted line (~1.01), then it will have a chance to grow because the equilibrium vapor pressure at its surface is less than the vapor pressure in the air. There will be a net transfer of water molecules from the air to the droplet. The droplet grows until it reaches Point B on the curve. If this droplet grows larger, its equilibrium vapor pressure will exceed the vapor pressure of the air, and it will begin to evaporate until its size shrinks to the diameter at Point B.

Figure 3.  Haze in Great Smoky Mountains National Park.

Consider the solution droplet in equilibrium at Point C in Figure 2. If the droplet is suddenly placed in an environment where the saturation ratio for air is 1.01, it can grow because the equilibrium vapor pressure for the droplet is less than the vapor pressure in the air. The droplet can grow indefinitely as long as the vapor supply in the air maintains the ratio of 1.01. To summarize, the hump in the Köhler curve represents a barrier to growth of solution droplets and sets a size limit for wettable haze particles in subsaturated air. If the air is supersaturated at a level above the Köhler curve and to the right of the hump, growth is unrestricted, and fog (cloud) droplets can form readily.

I discussed scattering of light by small particles in the January–February 2016 issue of Weatherwise on p. 39. To summarize very briefly, small particles in the atmosphere scatter (redirect) incoming light rays. Very small particles, whose sizes are less than 1/10 the wavelengths found in visible light (0.4 to 0.7 μm), scatter appreciably in all directions, and preferentially according to wavelength. Molecules of the air, whose sizes are very much smaller than wavelengths of visible light, scatter blue light (near 0.4 μm) much more strongly than red light (near 0.7 μm), giving a clear sky the familiar blue color. As the eye scans a clear sky in different directions, it senses the blue light scattered by air molecules from all directions. The backdrop for this view is outer space, which is black (devoid of light).

Figure 4.  Denver's “Brown Cloud” in this view of downtown Denver on the morning of December 31, 2015. The tops of the tall buildings are more easily visible than the bottoms, indicating a thicker haze close to the ground. The snow-covered foothills and mountains west of Denver are barely visible in the background. This haze appears slightly brown in the foreground but is more yellow beyond downtown, closer to the foothills.

Particles in the atmosphere considerably larger than the wavelengths in sunlight scatter strongly in the forward direction, i.e., in the same direction as the incident sunlight, and only weakly in the backward direction or out to the sides. The amount of scattering does not depend upon the wavelength, so that the incident and scattered light have the same mixture of wavelengths. Fog (cloud) droplets (size range 2–20 μm) fall into this category. If white light enters the fog, it remains white within the fog. Depending upon the intensity of the incident light and the thickness of the fog, the light may range from very bright to a dull gray, but the eye perceives no coloration.

Haze particles up to about 1 μm in diameter scatter more light in the forward direction than in other directions, and the scattering depends upon wavelength. Like air molecules, haze particles scatter blue light more than light at longer wavelengths, though the effect is not nearly so pronounced as with air molecules.

We often see atmospheric haze against a landscape, not the blackness of space. Our eyes sense light scattered toward us by air molecules and haze, and unscattered light coming to us directly from the landscape. As noted, the light scattered by haze tends toward the blue end of the spectrum, but light coming directly from the landscape can be any color. Viewed against a dark landscape such as a forest, haze can appear quite blue indeed. Figure 3, a photo taken in the Great Smoky Mountains National Park, is a good example. (The haze particles come mainly from isoprene emitted by the trees.)

Not much light comes from a dark forest, but appreciable light comes from brighter landscapes. Shorter-wavelength light from a bright landscape is preferentially scattered out of light rays traveling through the intervening atmosphere, so that the total light reaching our eyes may be shifted toward the red end of the spectrum. I suspect this may be a reason why haze near large cities and industrial areas sometimes acquires the name “brown cloud,” as is the case in Denver. Figure 4 is a photo of Denver's “brown cloud” when snow covered the ground. Because of the snow cover, the landscape is relatively bright. The haze is not very blue, but neither is it clearly brown—perhaps a light yellow-brown. In any case, some of the blue light coming from the landscape has apparently been scattered out by particles in the intervening atmosphere.

In summary, if visibility is restricted and the humidity is less than 100%, the restriction is probably caused by haze, especially if light from the scattering particles is subtly colored. Blue is the most likely color. If the visibility is severely restricted (less than one kilometer), and especially if the light from the scattering particles is white (from dazzling to dull gray), the cause is water-droplet fog.

I sometimes hear people say “It's too cold to snow.” I don't think this is true, but I'm not sure how to respond to them. Is there a threshold temperature for which it is truly too cold to snow?

Karen Garcia

Santa Fe, New Mexico

It is never too cold to snow, but sometimes it is too cold for heavy snow. Here's why.

The amount of water vapor in the atmosphere is temperature limited. The colder it is, the less vapor can exist in air. Figure 1 shows how saturation mixing ratio (the maximum possible value) varies with temperature in the range from −40°C to +10°C. Saturation mixing ratio is given in grams of water vapor per kilogram of dry air (g/kg). Its significance is that, if one tries to add more vapor to air that is already saturated at a given temperature, condensation will occur. The relationship is exponential, which means that, as the temperature rises, the maximum possible mixing ratio rises at an ever-increasing rate. Saturation vapor pressure at −40°C is only 0.08 g/kg. By −20°C it increases by nearly a factor of 10 to 0.78 g/kg. By 0°C, it increases by another factor of five to 3.84 g/kg.

Assume that the temperature is below freezing. Rising air cools. If vertical motion continues long enough, the air will become so cold that its actual vapor pressure will equal the saturation value. If any further lifting and cooling occurs, some of the vapor necessarily condenses, either into supercooled liquid droplets or into snow crystals. Snow clouds often contain both, except very cold ones, which contain only crystals. For the same reason that clouds can form at any temperature, so can the snow that clouds manufacture. Even in Antarctica at temperatures far below −40°C, a gentle fall of ice crystals is common.

Figure 1.  Saturation mixing ratio in grams of water vapor per kilogram of dry air (over liquid water) vs temperature in degrees Celsius (°C). Note the exponential increase of saturation mixing ratio with temperature.

Two factors can modulate snowfall rate. At a given temperature, stronger vertical drafts will produce a greater snowfall rate because the rates of cooling and condensation within a given air volume are greater. For a given updraft speed, snowfall will be greater when the temperature is higher because there is more water vapor to condense. For this reason, the most intense snowfalls occur when the air temperature is at or just below freezing.

Weatherwise Contributing Editor THOMAS W. SCHLATTER is a retired meteorologist and volunteer at NOAA's Earth System Research Laboratory in Boulder, Colorado. Submit queries to the author at weatherqueries@gmail.com, or by mail in care of Weatherwise, Taylor & Francis, 530 Walnut Street, Suite 850, Philadelphia, PA 19106.       

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