a sheet or stretch of ice forming on the surface of lakes and rivers when the temperature drops below freezing (0° C 【32° F】). The nature of the ice formations may be as simple as a floating layer that gradually thickens, or it may be extremely complex, particularly when the water is fast-flowing.

Much of the world experiences weather well below the freezing point, and in these regions ice forms annually in lakes and rivers. About half the surface waters of the Northern Hemisphere freeze annually. In warmer climates, waters may freeze only occasionally during periods of unusual cold, and in extremely cold areas of the world, such as Antarctica, lakes may have a permanent ice cover.

In most regions where ice occurs, the formation is seasonal in nature: an initial ice cover forms some time after the average daily air temperature falls below the freezing point; the ice cover thickens through the winter period; and the ice melts and decays as temperatures warm in the spring. During the formation and thickening periods, energy flows out of the ice cover, and, during the decay period, energy flows into the ice cover. This flow of energy consists of two basic modes of energy exchange: (1) the radiation of long-wavelength and short-wavelength electromagnetic energy (i.e., infrared and ultraviolet light) and (2) the transfer of heat (heat transfer) energy associated with evaporation and condensation, with convection between the air and the surface, and (to a lesser extent) with precipitation falling on the surface. While radiation transfers are important, the dominant energy exchange in ice formation and decay is the heat transfer associated with evaporation and condensation and with turbulent convection—the latter being termed the sensible transfer. Since these transfers of heat are driven by the difference between air temperature and surface temperature, the extent and duration of ice covers more or less coincide with the extent and duration of average air temperatures below the freezing point (with a lag in the autumn due to the cooling of the water from its summer heating and a lag in the spring due to the melting of ice formed over the winter).

As a general rule, small lakes freeze over earlier than rivers, and ice persists longer on lakes in the spring. Where there are sources of warm water—for example, in underground springs or in the thermal discharges of industrial power plants—this pattern may be disrupted, and water may be free of ice throughout the winter. In addition, in very deep lakes the thermal reserve built up during summer heating may be too large to allow cooling to the freezing point, or the action of wind over large fetches may prevent a stable ice cover from forming.

The setting for the development of ice cover in lakes is the annual evolution of the temperature structure of lake water. In most lakes during the summer, a layer of warm water of lower density lies above colder water below. In late summer, as air temperatures fall, this top layer begins to cool. After it has cooled and has reached the same density as the water below, the water column becomes isothermal (i.e., there is a uniform temperature at all depths). With further cooling, the top water becomes even denser and plunges, mixing with the water below, so that the lake continues to be isothermal but at ever colder temperatures. This process continues until the temperature drops to that of the maximum density of water (about 4° C, or 39° F). Further cooling then results in expansion of the space between water molecules, so that the water becomes less dense. This change in density tends to create a new stratified thermal structure, this time with colder, lighter water on top of the warmer, denser water. If there is no mixing of the water by wind or currents, this top layer will cool to the freezing point (0° C, or 32° F). Once it is at the freezing point, further cooling will result in ice formation at the surface. This layer of ice will effectively block the exchange of energy between the cold air above and the warm water below; therefore, cooling will continue at the surface, but, instead of dropping the temperature of the water below, the heat losses will be manifested in the production of ice.

The simple logic outlined above suggests that water at some depth in lakes during the winter will always be at 4° C, the temperature of maximum density, and indeed this is often the case in smaller lakes that are protected from the wind. The more usual scenario, however, is that wind mixing continues as the water column cools below 4° C, thereby overcoming the tendency toward density stratification. Between 4° and 0° C, for example, the density difference might be only 0.13 kilogram per cubic metre (3.5 ounces per cubic yard). Eventually some particular combination of cold air temperature, radiation loss, and low wind allows a first ice cover to form and thicken sufficiently to withstand wind forces that may break it up. As a result, even in fairly deep lakes the water temperature beneath the ice is usually somewhere below 4° C and quite often closer to 0° C. The temperature at initial ice formation may vary from year to year depending on how much cooling has occurred before conditions are right for the first initial cover to form and stabilize. In some large lakes, such as Lake Erie (Erie, Lake) in North America, wind effects are so great that a stable ice cover rarely forms over the entire lake, and the water is very near 0° C throughout the winter.

Before ice can form, water must supercool and ice crystals nucleate. Homogeneous nucleation (without the influence of foreign particles) occurs well below the freezing point, at temperatures that are not observed in water bodies. The temperature of heterogeneous nucleation (nucleation beginning at the surface of foreign particles) depends on the nature of the particles, but it is generally several degrees below the freezing point. Again, supercooling of this magnitude is not observed in most naturally occurring waters, although some researchers argue that a thin surface layer of water may achieve such supercooling under high rates of heat loss. Nucleation beginning on an ice particle, however, can take place upon only slight supercooling, and it is generally believed that ice particles originating from above the water surface are responsible for the initial onset of ice on the surface of a lake. Once ice is present, further formation is governed by the rate at which the crystal can grow. This can be very fast: on a cold, still night, when lake water has been cooled to its freezing point and then slightly supercooled on the surface, it is possible to see ice crystals propagating rapidly across the surface. Typically, this form of initial ice formation is such that the crystal c-axes are vertically oriented—in contrast to the usual horizontal orientation of the c-axis associated with later thickening. Under ideal conditions these first crystals may have dimensions of one metre or more. An ice cover composed of such crystals will appear black and very transparent.

If the lake surface is exposed to wind, the initial ice crystals at the surface will be mixed by the agitating effects of wind on the water near the surface, and a layer of small crystals will be created. This layer will act to reduce the mixing, and a first ice cover will be formed consisting of many small crystals. Whether it is composed of large or small crystals, the ice cover, until it grows thick enough to withstand the effects of later winds, may form and dissipate and re-form repeatedly. On larger lakes where the wind prevents a stable ice cover from initially forming, large floes may be formed, and the ice cover may ultimately stabilize as these floes freeze together, sometimes forming large ridges and piles of ice. Ice ridges generally have an underwater draft several times their height above water. If they are moved about by the wind, they may scour the bottom in shallower regions. In some cases—particularly before a stable ice cover forms—wind mixing may be sufficient to entrain ice particles and supercooled water to considerable depths. Water intakes tens of metres deep have been blocked by ice during such events.

Assuming that the heat flow through the ice equals the heat flow from the surface of the ice to the air above, the following formula for the thickening of ice may be fashioned:

In this formula h is the thickness of the ice, T_a is the air temperature, T_m is the freezing point, k is the thermal conductivity of ice (2.24 watts per metre kelvin), ρ_i is the density of ice (916 kilograms per cubic metre), L is the latent heat of fusion (3.34 × 10⁵ joules per kilogram), and t is the time since initial ice formation. The exact value of the bulk transfer coefficient (H_ia) depends on the various components of the energy budget, but it usually falls between 10 and 30 watts per square metre kelvin. Higher values are associated with windy conditions and lower values with still air conditions, but, with other information unavailable, a value of 20 watts per square metre kelvin fits data on ice growth quite well. The formula is particularly useful in predicting growth when the ice cover is thin. The first growth rate of the ice cover is proportional to the time since formation; as the ice thickens, however, the top surface temperature more closely approaches the air temperature, and growth proceeds proportional to the square root of time.

If there is a snow layer on top of the ice, it will offer a resistance to the flow of heat from the bottom of the ice surface to the air above. In this case, the incremental thickening rate (that is, the incremental thickening 【dh】 in an incremental time period 【dt】) may be predicted by the following formula:

where h_i is now the ice thickness with thermal conductivity k_i, and h_s is the snow thickness with thermal conductivity k_s. The thermal conductivity of snow depends on its density. It is greater at higher densities, ranging from about 0.1 to 0.5 watt per metre kelvin at densities of 200 to 500 kilograms per cubic metre, respectively.

When the weight of a snow cover is sufficient to overcome the buoyancy of the ice supporting it, it is usual for the ice to become submerged and for water to flow through cracks in the ice and saturate the snow, which then freezes. This mode of ice growth is different from that analyzed above, but it is quite common, and the ice so formed is known as snow ice. At typical snow densities, a layer of snow about one-half the thickness of the supporting ice will result in the formation of snow ice layers.

As the ice thickens, there is a tendency for crystals with a horizontal c-axis orientation to wedge out adjacent crystals with a vertical c-axis orientation and so become larger in diameter with depth. The resulting structure is one of adjacent columns of single crystals and is termed columnar ice. When a very thin section of the ice is cut and examined with light through crossed polaroid sheets, the crystal structure is clearly seen.

In the spring, when average daily air temperatures rise above the freezing point, ice begins to decay. Two processes are active during this period: a dimensional thinning and a deterioration of the ice crystal grains at their boundaries. Thinning of the ice layer is caused by heat transfer and by melting at the top or bottom surface (or both). Deterioration, sometimes called rotting or candling because of the similarity of deteriorating ice crystals to an assembly of closely packed candles, is caused by the absorption of solar radiation. When energy from the Sun warms the ice, melting begins at the grain boundaries because the melting point there is depressed by the presence of impurities that have been concentrated between crystal grains during the freezing process. Rotting may begin at the bottom or at the top, depending on the particular thermal conditions, but eventually the ice rots throughout its thickness. This greatly reduces the strength of the ice, so that rotten ice will support only a fraction of the load that solid, unrotted ice will support. Thinning and deterioration may occur simultaneously or independently of each other, so that sometimes ice thins without internal deterioration, and sometimes it deteriorates internally with little or no overall thinning. However, both processes usually occur before the ice cover finally breaks up.

Deteriorating ice has a gray, blotchy appearance and looks rotten. Because rotting takes place only by absorption of solar radiation, it progresses only during daylight hours. In addition, the presence of snow or snow ice, which either reflects most solar radiation or absorbs it rapidly in a thin layer, acts to prevent rotting of the ice below until the snow has been completely melted.

Melting of lake ice usually occurs first near the shorelines or near the mouths of streams. At these points of contact with inflowing warm water, the ice melts faster than it does at central lake locations, where most melting is caused by the transfer of heat from the atmosphere. Estimates of the rate at which thinning of the main ice cover occurs are usually based on a temperature index method in which a coefficient is applied to the air temperature above freezing.

Water temperature beneath the ice usually reaches its coldest at the time of freeze-up and then gradually warms throughout the winter. The warming is caused by the absorption of some solar radiation that has penetrated the ice cover, by the release of heat that has been stored in bottom sediments during the previous summer, and by warm water inflows. In deep lakes such warming is slight, while in shallow lakes it may amount to several degrees. After snow on the ice has melted in the spring, more solar radiation penetrates the ice cover, so that significant warming may occur. The mixing of warmed water with deteriorated ice is responsible for the very rapid clearing of lake ice at the end of the melt season. On most lakes, the timing of the final clearing of ice is remarkably uniform from year to year, usually varying by less than a week from the long-term average date of clearing.

The first appearance of lake ice follows by about one month the date at which the long-term average daily air temperature first falls below freezing. Ice appears first in smaller shallow lakes, often forming and melting several times in response to the diurnal variations in air temperature, and finally forms completely as air temperatures remain below the freezing point. Larger lakes freeze over somewhat later because of the longer time required to cool the water. In North America the Canadian-U.S. border roughly coincides with a first freeze-up date of December 1. North of the border freeze-up occurs earlier, as early as October 1 at Great Bear Lake in Canada's Northwest Territories. To the south the year-to-year patterns of freeze-up are ever more erratic until, at latitudes lower than about 45° N, freeze-up may not occur in some years.

In Europe the freeze-up pattern is similar with respect to air temperatures, but the latitudinal pattern shows more variation because much of western Europe is affected by the warming influence of the Gulf Stream. In Central Asia the latitudinal variation is more regular, with first freeze-up occurring about mid-January at 45° N and about October 1 at 72° N. Exceptions to these patterns occur where there are variations in local climate and elevation.

Because of the time required to melt ice that has thickened over the winter, the clearing of lake ice occurs some time after average daily air temperatures rise above freezing. Typically the lag is on the order of one month at latitude 50° N and about six weeks at 70° N. This pattern results in average clearing dates in mid-April at the U.S.-Canadian border and in June and July in the northern reaches of Canada.

The formation of ice in rivers is more complex than in lakes, largely because of the effects of water velocity and turbulence (turbulent flow). As in lakes, the surface temperature drops in response to cooling by the air above. Unlike lakes, however, the turbulent mixing in rivers causes the entire water depth to cool uniformly even after its temperature has fallen below the temperature of maximum density (4° C, or 39° F). The general pattern is one in which the water temperature fairly closely follows the average daily air temperature but with diurnal variations smaller than the daily excursions of air temperature. Once the water temperature drops to the freezing point and further cooling occurs, the water temperature will actually fall below freezing—a phenomenon known as supercooling. Typically the maximum supercooling that is observed is only a few hundredths of a degree Celsius. At this point the introduction of ice particles from the air causes further nucleation of ice in the flow. This freezing action releases the latent heat of fusion, so that the temperature of the water returns toward the freezing point. Ice production is then in balance with the rate of cooling occurring at the surface.

The particles of ice in the flow are termed frazil ice. Frazil is almost always the first ice formation in rivers. The particles are typically about 1 millimetre (0.04 inch) or smaller in size and usually in the shape of thin disks. Frazil appears in several types of initial ice formation: thin, sheetlike formations (at very low current velocities); particles that appear to flocculate into larger masses and exhibit a slushlike appearance on the water surface; irregularly shaped “pans” of frazil masses that, while appearing to be shallow, are actually of some depth; and (at high current velocities) a dispersed mixture or slurry of ice particles in the flow.

The supercooling of river water, while amounting to only a few hundredths of a degree Celsius or even less, provides the context for the particles to stick to one another, since under such conditions ice particles are inherently unstable and actively grow into the supercooled water. When they touch one another or some other surface that is cooled below the freezing point, they adhere by freezing. This behaviour causes serious problems at water intakes, where ice particles may adhere and then build up large accumulations that act to block the intake. In rivers and streams, frazil particles also may adhere to the bottom and successively build up a loose, porous layer known as anchor ice. Conversely, if the water temperature then rises above the freezing point, the particles will become neutral and will not stick to one another, so that the flow will be merely one of solid particles in the flowing water. The slightly above-freezing water may also release the bond between anchor ice and the bottom: it is not unusual for anchor ice to form on the bottom of shallow streams at night, when the cooling is great, only to be released the following day under the warming influence of air temperature and solar radiation.

As stated above, frazil forms into pans on the surface of rivers. Eventually these pans may enlarge and freeze together to form larger floes, or they may gather at the leading edge of an ice cover and form a layer of accumulating ice that progresses upstream. The thickness at which such an accumulation collects and progresses upstream depends on the velocity of the flow (V) and is given implicitly in the formula

in which g is acceleration of gravity, ρ and ρ_i are the densities of water and ice, respectively, h is the thickness of the accumulating ice, and H is the depth of flow just upstream of the ice cover. As a practical matter, floes arriving at the upstream edge will submerge and pass on downstream if the mean velocity exceeds about 60 centimetres (24 inches) per second. At certain thicknesses the ice accumulation may not be able to resist the forces exerted by the water flow and by its own weight acting in the downstream direction, and it will thicken by a shoving process until it attains a thickness sufficient to withstand these forces. During very cold periods, freezing of the top layer will provide additional strength by distributing the forces to the shorelines, so that thinner ice covers actually may be better able to withstand the forces acting on them.

As the ice cover accumulates and progresses upstream, it both adds resistance to the flow and displaces a certain volume of water. These two effects cause the depth of the river to be greater upstream, thus reducing the velocity and enabling further upstream progression to occur where previously the current velocity was too high to allow ice cover formation. This phenomenon is termed staging, by reference to its effect of increasing the water level, or “stage.” In the process there is a storage of water in the increased depth of the flow upstream, and this somewhat reduces the delivery of water downstream. The breakup of ice in the spring has the opposite effect—that is, the stored water is released and may contribute to a surge of water downstream.

Once the first ice cover has formed and stabilized, further growth is the same as with lake ice: typically columnar crystals grow into the water below, forming a bottom surface that is very smooth. This thickening may be predicted using equation (1), presented above for calculating the thickness of lake ice. An exception to this pattern arises when slightly above-freezing water flows beneath the ice cover. When this occurs, the action of the moving water either causes the undersurface to melt or retards the thickening. Since the rate at which melting occurs is proportional to the velocity times the water temperature, the ice cover over areas of higher velocity may be much thinner than in areas of lower velocity. Unfortunately, areas of thinner ice are often not apparent from above and may be dangerous to those traversing it.

In some rivers the initial formation of fixed ice takes place along the shorelines, with the central regions open to the air. The shore ice then gradually widens from the shoreline, and either the central region forms as described above by accumulation of frazil or the two sides of shore ice join.

In larger, deeper rivers, frazil produced in upstream reaches may be carried downstream and be transported beneath the fixed ice cover, where it may deposit and form large accumulations that are called hanging dams. Such deposits may be of great depth and may actually block large portions of the river's flow. In smaller, shallower streams, similar ice formations may be combinations of shore ice, anchor ice deposits, small hanging-dam-like accumulations, and (over slower-flowing areas) sheet ice.

Ice in smaller streams shows more variation through the winter, since most of the water comes from groundwater inflows during periods between rain. Groundwater is warm and over time may melt the ice formed during very cold periods. At other times all the water in a small stream freezes; subsequent inflowing water then flows over the surface and freezes, forming large buildups of ice. These are known as icings, Aufeis (German), or naleds (Russian). Icings may become so thick that they completely block culverts and in some cases overflow onto adjacent roads.

In late winter, as air temperatures rise above the freezing point, river ice begins to melt owing to heat transfer from above and to the action of the slightly warm water flowing beneath. As occurs in lake ice, river ice also may deteriorate and rot because of absorption of solar radiation. On the undersurface, the action of the turbulent flowing water causes a melt pattern in the form of a wavy relief, with the waves oriented crosswise to the current direction. Eventually, if the ice cover is not subjected to a suddenly increased flow, it may melt in place with little jamming or significant rise in water level. More likely, however, the ice may be moved and form ice jams.

During the spring in very northern areas, and during periods of midwinter thaw in more temperate areas, additional runoff from snowmelt and rain increases the flow in the river. The increased flow raises the water level and may break ice loose from the banks. It also increases the forces exerted on the ice cover. If these forces exceed the strength of the ice, the cover will move and break up and be transported downstream. At some places the quantity of ice will exceed the transport capacity of the river, and an ice jam will form. The jam may then build to thicknesses great enough to raise the water level and cause flooding. Typically, jams form where the slope of the river changes from steeper to milder or where the moving ice meets an intact ice cover—as in a large pool or at the point of outflow into a lake.

Spring breakup jams are usually more destructive than freeze-up jams because of the larger quantities of ice present. Besides causing sudden flooding, the ice itself may collide with structures and cause damage, even to the point of taking out bridges. Sometimes a jam forms, water builds up above it, and the jam breaks loose and moves downstream only to form again. This process may repeat itself several times. In northerly flowing rivers such behaviour is typical, since the upstream ice is freed first and moves toward colder, more stable ice covers.

There are a variety of means of modifying ice in rivers. Icebreaking vessels are used to clear paths for other vessels and occasionally to assist in relieving jams on large rivers. Icebreakers are used extensively in northern Europe and to some extent on the Great Lakes and St. Lawrence River of North America. Dusting the ice cover with a dark material such as coal dust or sand can increase the absorption of solar radiation and thus create areas of weakness that aid in an orderly breakup. Dusting has limited effectiveness, however, if a later snowfall covers the dust layer. Trenching of the ice cover with a ditching or similar machine has been practiced to create a weak zone in areas that are historically prone to jamming. Once ice jams have formed, they are sometimes blasted with explosives; (explosive) however, if there is no current to transport the ice away after blasting, such measures are usually of little effect.

Ice-retention structures such as floating ice booms are used to hold ice in place and prevent it from moving downstream, where it might cause problems. There have been some attempts to control water releases from dammed reservoirs (reservoir) so as to induce breakup in an orderly manner, but these measures are limited to a narrow range of conditions. Air bubbler systems and flow developers (submerged motor-driven propellers) are used to melt small portions of the ice cover by taking advantage of any thermal reserve, relative to the freezing point, that may exist in the water. These are usually more successful in lakes or enclosed areas than in rivers, since the water temperature in rivers is rarely much above the freezing point.

Wastewater from the cooling of power plants, both fossil-fueled and nuclear, has sometimes been suggested as a source of energy for melting ice downstream of the release points. This method may be advantageous in small areas, but the power requirements for melting extended reaches of ice are immense. Discharges from smaller sources, such as sewage treatment plants, are generally too small to have more than a very localized effect. On the other hand, the water held in reservoirs is often somewhat warmer than freezing, and it can be released in quantities sufficient to result in extended open water downstream—the precise distance depending on how much surface area is required to cool the water back to the freezing point by heat loss to the cold air above.

Dates of first freeze-up of rivers follow patterns similar to those of lakes, with a tendency for rivers to freeze over somewhat later than smaller lakes. The many factors that affect the freezing process of rivers make generalizations difficult, however. Slower poollike reaches may freeze over, while more rapidly flowing reaches may remain open well into the winter. Breakup is even more erratic, particularly in the more temperate zones where midwinter thaws may cause a breakup that is followed by another freeze-up and a later breakup as spring temperatures arrive. As a general rule, rivers break up in response to runoff from snowmelt or rain well before lakes clear of ice—although the first shoreline melting in lakes occurs at about the same times as river breakup. In north-flowing rivers, especially in central Russia and western Canada, breakup occurs first in upstream, southerly reaches and then progresses northward with the movement of the spring thaw.