Snowpack Properties, Evolution and Ablation • The discussion in the preceding lectures has emphasized the various processes of metamorphism that control the snow bulk properties. • Thermal properties that depend only on density (specific heat, latent heat) are well defined. 1 • However, those that depend on conductivity or permeability of the snowpack are affected by sintering, particle size, ice layers and depth hoar. • • The specific and latent heats of snow are the simplest thermal properties to determine since the contributions from air and water vapour can be discounted; each property is simply the product of the snow density and the corresponding property for ice. 2 • The temperature dependence of the specific heat of ice given by Dorsey (1940) is: • C = 2.115 + 0.00779T • where C is the specific heat (kJ kg-1 K-1), and T (oC) is temperature. • The latent heat of melting of ice at 0 oC and standard atmospheric pressure is 333.66 kJ kg-1. 3 • For one-dimensional, steady-state heat flow by conduction in a solid the thermal conductivity is the proportionality constant of the Fourier equation: • F = -K dT/dz • where F is the heat flux (W m-2) and dT/dz is the temperature gradient. • The thermal conductivity of snow (K) is a more complex property than specific heat because its magnitude depends on such factors as the density, temperature and the microstructure of the snow. 4 • The thermal conductivity of ice varies inversely with temperature by about 0.17% oC-1; the same may be expected for snow. • A temperature gradient could induce a transfer of vapour and the subsequent release of the latent heat of vapourization, thereby changing the thermal conductivity value. 5 • In non-aspirated dry snow the heat transfer process involves: conduction of heat in the network of ice grains and bonds, conduction across air spaces or pores, convection and radiation across pores (probably negligible) and vapour diffusion through the pores. • Because of the complexity of the heat transfer processes, the thermal conductivity of snow is generally taken to be an “apparent” or “effective” conductivity Ke to embrace all the heat transfer processes. 6 • The degree of surface packing (for example, hardness) also affects the flow of heat through snow, probably because a surface crust of low air permeability inhibits ventilation in the upper snow layer. • The thermal conductivity of snow, even when dense, is very low compared to that of ice or liquid water; therefore snow is a good insulator. • This is an important factor affecting heat loss from buildings and the rate of freezing of lake and river ice. 7 • Typical numerical models of snow use three prognostic variables to define a snowpack: snow depth, snow water equivalent, and temperature. • From snow depth and snow water equivalent, one can infer the snow density from: • ρs = ρw(w/s) • where w (m) is the snow water equivalent, s (m) is the snow depth, and ρs and ρw are the snow and water densities, respectively. 8 Source: Sun et al. (2004) 9 • Apart from snow depth and snow water equivalent, the heat content or temperature of the snowpack is required to describe the system completely. • The snow temperature is directly related to its heat content H (J) by: • T = H/(ρw w C). • The energy balance of a snowpack is complicated not only by the fact that shortwave radiation penetrates the snow but also by water movement and phase changes. 10 Source: Lynch-Stieglitz (1994) 11 • The energy balance of a snow volume depends upon whether it is a “cold” (< 0oC) or a “wet” (0oC, often isothermal) snowpack. • Recall the energy balance of the snowpack: • Q* + QP = QH + QE + QG + ΔQS + QM. • A term is added here to the energy balance to consider the heat transported by precipitation (QP), either snowfall or rainfall. 12 • In the case of a cold snowpack, such as is commonly found in mid-latitudes during winter with little or no solar input, QE and QM are likely to be negligible. • Similarly, heat conduction within the snow will be small because of the low thermal conductivity of snow and the lack of solar heating, so that ΔQS and QG are also negligible. • The energy balance therefore reduces to that between a net radiative sink Q* and a convective sensible QH heat source. 13 • Although snowcover reduces the available energy at the surface because of its high albedo to solar radiation and high emissivity of longwave radiation, its insulative properties exert the greatest influence on soil temperature regime. • Snow acts as an insulating layer that reduces the upward flux of heat, resulting in higher ground temperatures than would occur if the ground was bare. 14 • In Canada, average ground temperatures are about 3oC warmer than average air temperatures. • In the case of a “wet” snowpack during the melt period, the surface temperature will remain close to 0oC, but the air temperature may be above freezing. • Since snow is porous, liquid water infiltration is also important in transporting energy within the snowpack and into soils. 15 • If meltwater freezes within the snowpack, there is latent release, warming snowpack layers to the freezing point. • Most of the energy exchanges between snow and its environment occur at the atmosphere or ground interfaces; however, because snow is porous, some radiation and convective fluxes that occur within the top few centimetres of the snowpack. 16 • The important fluxes that can directly penetrate the snowpack are radiation, conduction, convection, and meltwater or rainwater percolation. • Temperature regimes in dry snowpacks are exceedingly complex and are controlled by a balance of the energy regimes at the top and bottom of the snowpack, radiation penetration, effective thermal conductivity of the snow layers, water vapour transfer, and latent heat exchange during metamorphism. 17 • Temperature stratification within dry snowpacks is usually unstable (warm temperatures below cold temperatures) from formation until late winter and spring, as energy inputs from the soil boundary exceed those from the atmosphere and upper layers. • As a result, temperatures become warmer with depth, with gradients as high as 50 oC m-1 in shallow subarctic and arctic snowpacks during early midwinter. 18 • In cold climates with frozen soils, an inversion can develop in late winter where the upper snowpack warms to higher temperatures than the lower layers; this reflects higher energy inputs from the atmosphere (often due to long sunlit periods in the northern spring) than from the frozen soil. • For a given climate, the thermal regime in the snowpack strongly depends on the amount of snowfall early in the winter season. 19 • Heavy snowfall early in the winter will tend to maintain the snowpack relatively warm, whereas shallow snowcovers will adjust more rapidly to the air temperatures. • For a deep snowpack a midwinter rainfall would increase density and decrease depth. • Subarctic and arctic snowpacks can undergo melt in upper layers whilst maintaining snow temperatures significantly below the freezing point in the lower layers. 20 • Internal heat fluxes in wet snow, or in partially wet snow, are principally driven by conduction and by latent heat release due to refreezing of liquid water. 21 22 Ref: Bartelt and Lehning (2002) 23 Ref: Bartelt and Lehning (2002) Source: Stieglitz et al. (2003) 24 25 Source: Stieglitz et al. (2003) 26 Source: Pomeroy and Brun (2001) Snowpack Ablation • In many countries snow constitutes a major water resource; its release in the form of melt water can significantly affect agriculture, hydro- electric energy production, urban water supply and flood control. • The ablation of a snowcover or the net volumetric decrease in its snow water equivalent is governed by the processes of snowmelt, evaporation and condensation, the vertical and lateral transmission of water within the snowcover and the infiltration of water to the underlying ground. 27 • In turn, water yield and streamflow runoff originating from snow are governed by these same processes as well as the storage and the hydraulics of movement of water in channels. • The rate of snowmelt is primarily controlled by the energy balance near the upper surface, where melt normally occurs. • Shallow snowpacks may be considered as a “box” to which energy is transferred by radiation, convection, and conduction. 28 • Early in the melt sequence vertical drainage channels develop in the snow contributing further to its heterogeneity. • The internal structure significantly influences the retention and movement of melt water through the snow, making a detailed analysis of the transmission process extremely difficult. • When the pack is primed to produce melt it is at a temperature of 0oC throughout and its individual snow crystals are coated with a thin film of water; also, small pockets of water may be found in the angles between contacting grains, usually amounting to 3 to 5% of the snow by weight. 29 • Any additional energy input produces melt water which subsequently drains to the ground. • When melt rates are at their highest, 20% (by weight) of the pack or more may be liquid water, most of which is in transit through the snow under the influence of gravity. • The amount of energy available for melting snow is determined from the energy budget equation. 30 Shortwave Radiation • There are two main types of radiation affecting snowmelt: shortwave and longwave radiation. • The amount of solar radiation penetrating the earth's atmosphere to be received at the surface varies widely depending on latitude, season, time of day, topography (slope and orientation), vegetation, cloud cover and atmospheric turbidity. 31 • While passing through the atmosphere radiation is reflected by clouds, scattered diffusely by air molecules, dust and other particles and absorbed by ozone, water vapour, carbon dioxide and nitrogen compounds. • The absorbed energy increases the temperature of the air, which in turn, increases the amount of longwave radiation emitted to the earth's surface and to outer space. 32 • Short-wave radiation reaching the surface of the earth has two components: a direct beam component along the sun's rays and a diffuse component scattered by the atmosphere but with the greatest flux coming from the direction of the sun. • • Figure 9.1 shows the annual variation in daily values of solar radiation received by a horizontal surface at several latitudes assuming a mean transmissivity of unity, implying that all the energy reaches the surface. • The influence of transmissivity is illustrated in Figure 9.2. 33 34 35 Source: Gray and Male (1981) 36 • The time of year obviously is an important factor governing the solar radiation flux incident on the earth's surface, and hence on the melt rate. • As a rule, the longer the spring melt is delayed the greater the danger of flooding. • This is due partly to increases in the radiative flux and partly to the increased probability of rain. 37 • The transmissivity is highest in winter and lowest in summer because the atmosphere contains more water vapour during summer. • It also varies somewhat with latitude, increasing northwards. • Snow on a south-facing slope melts faster than snow on a north-facing slope, the reason being that the orientation of the slope affects the amount of direct beam solar radiation the area receives. 38 • The results are symmetric about a north- south line; as might be expected the influence of orientation diminishes towards the summer solstice. • Even on a 10o slope the effect of orientation can be significant; e.g., at 50 oN on April 1, a south-facing slope receives approximately 40% more direct beam radiation than a north-facing slope. 39 40 41 42 Longwave Radiation • The net longwave radiation at the snow surface L* is composed of the downward radiation L↓ and the upward flux L↑ emitted by the snow surface. • Over snow L↑ is normally greater than L↓ so that L* represents a loss from the snowpack. • The longwave radiation emitted by the snow surface is calculated with the Stefan-Boltzmann law on the assumption that snow is a near perfect black body in the longwave portion of the spectrum. 43 • In alpine areas topographical variations have a significant influence on the longwave radiation received at a point, e.g., in a valley the atmospheric radiation is reduced because a part of the sky is obscured by its walls. • However, the valley floor will gain longwave radiation from the adjacent slopes in amounts governed by their emissivities and temperatures; the reflected longwave radiation from snow and most natural surfaces is almost negligible. • Thus in areas of high relief the radiation incident at a site includes longwave emission from the atmosphere and the adjacent terrain. 44 • To a first approximation the radiation emitted by cloud can be obtained by assuming black-body emission at the temperature of the cloud base. • Hence, the net longwave radiation exchange between the overcast sky and the snow can be approximated as an exchange between two black bodies having temperatures Ts (snow surface) and Tc (cloud base), i.e., L* = σ(Tc4 - Ts4). 45 Sensible, Latent, and Ground Heat Fluxes • The convective and latent energy exchanges, Q h and Qe, respectively, are of secondary importance in most snowmelt situations when compared to the radiation exchange, but still need to be considered to assess melt rates. • Both Qh and Qe are governed by the complex turbulent exchange processes occurring in the first few metres of the atmosphere immediately above the snow surface. 46 • Heat is transferred to the snow by convection if the air temperature increases with height (commonly occurring when the snow is melting); and water vapour is condensed on the snow (accompanied by release of the latent heat of vapourization) if the vapour pressure increases with height. • The ground heat flux QG is a negligible component in daily energy balances of a snowpack when compared to radiation, convection or latent heat components, so that the total snowmelt produced by QG over short periods of time can be ignored. 47 • However, QG does not normally change direction throughout the winter months and consequently its cumulative effects can be significant over a season. • In areas where snow temperatures remain near the freezing point and ground temperatures are relatively warm, melt can be produced as a result of QG. • Although the amount of water produced may be small, its resultant effect on the thermal properties and infiltration characteristics of the underlying soil may be important. 48 • Heat exchanges between soils and snow follow the simple Fourier equation for heat transfer used in heat transfer in snow alone. 49 Rain on Snow • The heat transferred to the snow by rain water is the difference between its energy content before falling on the snow and its energy content on reaching thermal equilibrium within the pack. • Two cases must be distinguished in this energy exchange: 50 • 1) Rainfall on a melting snowpack where the rain does not freeze; • 2) Rainfall on a pack with temperature < 0 oC where the water freezes and releases its latent heat of fusion. • The first case can be described by the expression: • QP = ρw Cp(Tr - Ts)Pr/1000 • where QP is the energy supplied by rain to the snowpack, ρw is the density of water, Cp is the heat capacity of water, Tr the temperature of the rain, Ts is the snow temperature, Pr is the depth of rain or precipitation rate. 51 Units • QP (kJ m-2 d-1) • ρ (kg m-3) • Cp (kJ kg-1 oC-1) • Tr (oC) • Ts (oC) • Pr (mm d-1) 52 • When rain falls on a snowpack which has a temperature <0oC, the situation is more complicated since the pack freezes some of the rain thereby releasing heat by the fusion process. 53 Snowmelt • The amount of meltwater can be calculated from: • wm = QM /(ρw Lf B) • where wm is the meltwater (m), Lf (J kg-1) is the latent heat of fusion, and B is the fraction of ice in a unit mass of wet snow. • B usually has a value of 0.95 to 0.97. 54 • Net radiation and sensible heat largely govern the melt of shallow snowpacks in open environments. • At the beginning of the melt, radiation is the dominant flux with sensible heat growing in contribution through the melt. 55 • If a complete set of meteorological measurements is not available, then temperature index models may be used to predict snowmelt. Index models relate melt to air temperatures such that: • wm = Mf (TA - TB) • where TA (oC) is the mean air temperature over a given time period and TB is a base temperature below which melt does not occur (usually 0oC). • The melt factor Mf varies from 6 to 28 mm oC-1 day-1 for snowmelt on the Canadian Prairies. 56 • Although index models are simple, they should be used with caution as the melt factors tend to vary from year to year and with location. 57 Streamflow Generation • Streamflow generated by snowmelt water that directly runs off rather than infiltrating or from water that infiltrates and then moves downslope through a shallow subsurface soil of high permeability. • During snowmelt, frozen or saturated soils restrict infiltration and evaporation is relatively low; this promotes a water excess over a basin and permits relatively large runoff generation for the amount of water applied to the ground. 58 • As a result, peak annual streamflows often occur directly after snowmelt. • The constituent water of this freshet comprise both snowmelt water and water expelled from soils by infiltrating snowmelt water, with important implications for stream chemistry. • For point scales, the influence of snow water equivalent on infiltration and runoff generation varies for different soil types. 59 • The effect of a deep forest environment snowpacks in promoting warm soils causes forest runoff to drop with increasing snow water equivalent for deep snow and dry soils. • In northern forests, from 40 to 60% of annual streamflow is derived from snowmelt, with increases in snowmelt runoff of from 24 to 75% when the forest is removed by harvesting or fire. • In cold, semiarid environments (arctic, northern prairies, steppes), greater than 80% of annual streamflow is derived from snowmelt, even though snowfall accounts for less than 50% of the annual precipitation. 60 • Snowmelt in the western cordillera of North America and mountain systems of central Asia is the major source of water when carried as streamflow to semiarid regions downstream. • Snowmelt water sustains arctic, alpine, prairie, and boreal forest lakes and wetlands, which are primary aquatic habitats in their respective ecosystems. 61 Ref: Barnett et al. (2005) 62 Annual Cycle of River Discharge Source: Yang et al. (2003), JGR. 63 Source: Déry et al. (2005), J. Climate. Annual cycle of mean daily discharge 64 Latitudinal Variation of HJUB Freshets JD = 5(Latitude) -126 65 Source: Déry et al. (2005), J. Climate.
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