Snow and runoff

The role of snowmelt in the hydrologic cycle is defined by the response of snow to radiant energy. Snow stores water at the Earth's surface for various periods, and snowmelt has a delayed effect on a discharge hydrograph because snowfall does not influence streamflow until the snow melts. Seasonal snowpack melting is related to the snowpack radiation balance which supplies the energy to convert snow into liquid water. However, the radiation balance depicted by Equation 2.11 requires expansion when applied to a snow surface due to the relatively complex nature of snow compared to other surface materials.

6.11.1 Radiation balance and snow

The snow surface is semitransparent to solar radiation, and this allows transmission of shortwave radiation into the snowpack. Radiation absorption then occurs within a volume rather than being limited to a plane coincident with the snow surface. This radiation transmission and absorption characteristic influences the nature of both the radiation balance and the energy balance of snow.

Shortwave radiation incident at the snow surface is greater than that at any depth. The decay of the flux with distance into the snow follows an exponential curve defined by Beer's law

1200 1000 800 600 400 200 0

Longwave atmospheric >

----.. ___- Solar radiation

\

/

/ f

Albedo ^^

Longwave

terrestrial

100 400 700 1000 1300 1600 1900 2200 Time

100 400 700 1000 1300 1600 1900 2200 Time

Fig. 6.9. Radiation balance for a snowcovered surface on 22 April 1954, a clear day, at the Central Sierra Snow Laboratory just west of the crest of the Sierra Nevada in California (40° N, elevation 2273 m). (Developed from data reported by the U.S. Army Corps of Engineers, 1956.)

where K#z is shortwave radiation at depth z, K#o is shortwave radiation at the surface, e is the base of natural logarithms, and a is the extinction coefficient (m-1). The attenuation or depletion of shortwave radiation with depth in the snowpack is directly related to the extinction coefficient. The value of the extinction coefficient depends on the physical characteristics of the transmitting medium and the wavelength of the radiation. Consequently, the extinction coefficient of shortwave radiation is greater for snow than for ice because of the difference in the physical medium. Shortwave penetration may be 1 m in snow and 10 m in ice (Oke, 1987).

Snow albedo is another important radiative characteristic of snow. Albedo can change from 0.25 to 0.80 in a few hours with the deposition of a thin snowcover. The albedo of the snow surface may then decrease from 0.80 to 0.40 in a matter of days as the snow ages. Albedo varies with wavelength within the shortwave portion of the spectrum, but the highest albedo is for the shortest wavelengths. Albedo decreases to quite low values in the near-infrared wavelengths. The high albedo of snow at the shortest wavelengths is the reverse of the condition for most soil and vegetation surfaces (Oke, 1987).

In general, the daytime net radiation surplus for a snow surface is small compared with most other natural surfaces. Snow's high albedo results in little shortwave radiation absorption. Even a portion of the shortwave radiation transmitted into the snowpack is reflected and contributes to the high albedo. Absorption of the radiation transmitted into the snowpack does not offset the stronger influence of the shortwave loss due to albedo. In the longwave portion of the spectrum, the absolute magnitude of L" is usually relatively small because the snow surface temperature is low, but the L# flux is also small (Fig. 6.9). The result is a small net longwave loss, and combined with the small shortwave surplus results in a small net radiation surplus.

Equation 2.11 best portrays surface conditions where radiation fluxes are a function of solar angle and latitude and a steady-state atmospheric boundary layer (Pomeroy et al., 2003). Snow-covered grasslands, plains, and tundra approximate these conditions, but snow in mountainous terrain represents a more complex problem because a portion of the sky is obscured by surrounding topography. In addition, an alpine snow surface receives radiation reflection and emission from surrounding topography (Pliiss and Ohmura, 1997). In mountainous terrain the snow radiation balance takes the form

Rn = (Is + Ds + Dt)(1 - a) +La| +Lt# -L" (6.6)

where Is is direct solar radiation, Ds is diffuse solar radiation, Dt is diffuse solar radiation from the surrounding terrain, Lt is the incoming longwave radiation from the surrounding terrain, and the other variables are defined for Equation 2.11. All units are in Wm-2 except for a which is dimensionless. In mountainous terrain, longwave radiation from surrounding topography can make an important contribution to the surface radiation balance. Since longwave radiation is present day and night, its influence on the radiation balance is significant in understanding areal variations in the energy balance and snowmelt. Slope and aspect are additional important considerations because they affect snow accumulation, snowmelt energetics, meltwater fluxes, and runoff contributing area (Pomeroy et al., 2003).

6.11.2 Energy balance and snowmelt

Much of the current knowledge of the energy balance and melt characteristics of snow can be traced to the work of the U.S. Army Corps of Engineers (1956). The energy balance of snow is complicated by the penetration of shortwave radiation into the snowpack and by internal water movement and phase changes within the snowpack. Viewing the snowpack as a volume helps to understand the energy fluxes and the physical changes that occur in the snow-pack as the melt process occurs.

The traditional energy balance (Equation 2.12) is typically rewritten for a snow surface to include terms describing energy sources available to melt snow. The energy for snowmelt comes from net radiation, conduction and convection transfers of sensible heat from the overlying air, condensation of water vapor from the overlying air, conduction from the underlying soil, and from rainfall. The relationship is represented by

where SNm is the energy available for snowmelt, D is energy transported to the snowpack by snow or rain, and all other variables are defined for Equation 2.12. All units are in Wm-2. The position of Rn in Equation 6.7 acknowledges that net all-wave radiation is the dominant energy component responsible for snowmelt (PHiss and Ohmura, 1997; Suzuki and Ohta, 2003). Net radiation has a maximum absorption just below the surface during the day (Oke, 1987). Consequently, the plane of greatest energy, the highest temperature, and the greatest potential mass flux are not coincident with the snow surface. At night, with only longwave radiative exchanges, the active surface is at or near the snow surface. This produces a sharp temperature gradient in the upper layer of the snow largely due to the low thermal conductivity of snow. The snow surface becomes very cold because radiative losses are not offset by heat flows from within the snowpack.

Snow is an effective insulating cover for the ground. As little as 0.1 m of fresh snow will insulate the underlying ground. Large radiation variations are limited to the snowcover because snow has low heat conductivity. Surface radiative losses are not replaced quickly by heat fluxes from below. The strong cooling of the atmosphere near the Earth's surface stabilizes the atmosphere against convection and contributes to the occurrence of colder local temperatures. During summer daylight hours, snow quickly comes to a uniform temperature of 0 °C throughout the snowpack. This is due to penetration of the strong shortwave radiation and percolation of water to deeper layers that assist in transferring heat within the snowpack.

The melt process is especially important hydroclimatically because it represents the return of moisture to the liquid phase, and it involves energy fluxes that are climatically driven. Snow undergoes a continuous metamorphism until it melts, and the metamorphic changes are driven by the energy state of the snowpack. A centimeter of water melted in a snowpack at 0 °C requires 39 Wm-2 of energy.

The conversion of snow to water is known as ablation. At this time, the mass of the snowpack is reduced in response to the loss of water. Ablation can be thought of as the opposite of the accumulation stage during which the snow-pack increases. Melt or ablation of the snowpack does not occur as long as the energy balance is negative and SNm < 0. This condition cools the snowpack and increases the snow "cold content'' or the amount of energy required to bring the entire snowpack to 0 °C. A positive energy balance results in SNm > 0, and this adds energy to the snowpack and produces warming of the snow until the entire snowpack is isothermal at 0 °C. Snowmelt does not occur in significant amounts until the entire snowpack is isothermal at 0 °C, but once this condition is reached SNm > 0 results in melt (Marks and Winstral, 2001). The ablation period of a seasonal snowpack is divided into three phases once a sustained positive net energy input supports SNm > 0 continuously.

The snowpack first experiences warming when the average snowpack temperature increases more or less steadily until the snowpack is isothermal at 0 °C. It is important to note that no melting occurs, rather the snowpack temperature changes. The heat required to raise the snowpack average temperature to the melting point before melt occurs defines the cold content of the snow. The cold content (SNcc) is expressed as

where ci is the heat capacity of ice at 0 °C (2.05 J g-1 K-1), pw is the mass density of water (1.00 gcm-3), hm is the water equivalent of the snowpack (cm), Ts is the average temperature of the snowpack (°C), and Tm is the melting point temperature (0 °C) (Dingman, 1994). The cold content expresses the energy required to raise the snowpack temperature to the melting point, and it can be determined anytime before melt begins.

Snowpack ripening occurs as additional energy warms the snowpack after it is isothermal. Ripening produces meltwater that is initially retained in the pore spaces of the snow grains by surface-tension forces. No meltwater is released from the snowpack during this stage, but at the end of this phase the snowpack is isothermal at 0 °C. Under this condition, the snowpack is considered to be ripe and cannot retain any more liquid water within the snowpack. The energy necessary to bring a snowpack to a ripe condition (SNr) is equal to the cold content plus the latent heat required by the amount of melt produced and is represented by

where 0ret is the maximum volumetric water content that the snow can retain and is estimated from empirical studies, hs is the depth of the snowpack, pw is the mass density of water (1.00gcm-3), and 1f is the latent heat of fusion (3.35 x 105Jkg-1) (Dingman, 1994).

After the snowpack is ripe, any further energy inputs produce water releases from the snowpack. Additional meltwater cannot be held by surface tension against the pull of gravity within the snowpack after the ripe condition is reached. Water begins to percolate downward ultimately to become water output. The net energy input required to complete the output phase is the amount of energy needed to melt the snow remaining at the end of the ripening phase (SNo) and is computed as

where h^t is the liquid water retaining capacity of the snowpack (cm), and all other variables are defined previously (Dingman, 1994).

In many situations, the snowpack does not progress steadily through this sequence. Some melting occurs at the surface of a snowpack prior to the ripening phase (Ward and Robinson, 2000). The meltwater percolates into the cold snow at depth and refreezes releasing latent heat that raises the snow temperature. Nevertheless, the three-phase structure provides a useful framework for describing the process and understanding how the energy balance of the snowpack drives the ablation process. The amounts of net energy required for each of the melt phases are readily computed. Streamflow contributed by snowmelt is thus likely to occur during clear sky conditions and produces a hydrograph with lower peak flows but sustained high flows.

6.11.3 Thermal indices and snowmelt

Snowmelt can be computed using heat conservation principles outlined in the previous section, but it is difficult and expensive to fulfill the data requirements of the energy balance of the snowpack. An empirical temperature index approach has a long history of use for estimating snowmelt largely because air temperature is often the only reliable and consistently available weather variable measured for remote areas, and it is well correlated with radiation, wind, and humidity so that residual errors are usually not a factor (Luce, 1995). However, Ohmura (2001) asserts there is a physical basis for air temperature as an effective parameter for estimating snowmelt that is evident when Rn in Equation 6.7 is expressed as individual terms. The expanded form of the energy balance is

SNm = K#(1 - a)+L # - £<jT4 + H + LE + G + D (6.11)

where £ is the emissivity of snow with a value close to one, and all other terms are defined previously. The K# and L# terms depend on the composition and temperature of the overlying atmosphere and on the relief of the surrounding topography as discussed for Equation 6.6. The aT4 term is fundamentally different from all the other terms on the right side of the equation in that it is determined entirely by the other terms which represent external fluxes. The aT4 term adjusts in response to the other fluxes by altering the radiative emission rate to obtain a new equilibrium. The longwave surface emission is a function of surface temperature corresponding to the equilibrium state. There are mutual dependencies of different degrees between other terms in equation 6.11, but aT4 is not autonomous nor can it alter itself spontaneously as is the case for the other terms. Since atmospheric longwave radiation is the dominant heat source for snowmelt, its relationship with aT4 in forming the longwave radiation balance defines a close physical coupling between surface temperature and snowmelt that establishes air temperature as a significant index for estimating melt (Ohmura, 2001).

A common temperature index approach for estimating daily snowmelt (SNmd) is where k' is a melt coefficient or melt factor in mm °C-1 that varies with latitude, elevation, slope inclination and aspect, forest cover, and time of the year and must be empirically estimated for a given site, Ta is the air temperature in °C, and Tb is the reference temperature usually taken as the snow melting point temperature, 0 °C. In the absence of site-specific data, k' can be estimated using various generalized expressions incorporating common site factors (Dingman, 1994). The temperature index approach has been applied with success for spring snowmelt over large basins (Luce, 1995), but temperature indices have not been successful for estimating snowmelt from open grasslands or for small basins at high elevations (Linacre, 1992).

Mathematically, Equation 6.12 implies that melt occurs when Ta > 0 °C, which is not always true (Bras, 1990). The energy balance of a snowpack indicates snowmelt can occur for air temperatures below 0 °C, especially during clear, calm days when solar radiation dominates the energy balance. Also, no melt can occur on clear nights when outgoing longwave radiation is significant even though the air temperature is above 0 °C.

Forest cover is probably the most common factor used in developing a melt coefficient for Equation 6.12. Forest cover serves as a surrogate because it has a significant effect on many of the variables affecting the snowcover energy balance (Suzuki and Ohta, 2003). Climatic factors are important in accounting for differences when physiographic conditions are constant (Marks and Winstral, 2001).

The degree-day method for estimating daily snowmelt is based on empirical evidence that daily snowmelt is expressed as a linear function of average air temperature. A degree-day is a departure of one degree per day in the daily mean temperature from a reference temperature. In general, it is assumed that there is no melt for temperatures below freezing and that melt is directly proportional to the number of degrees above freezing. Degree-day snowmelt for one day (SNmdd) in mm is expressed as where Df is a degree-day factor in mm °C-1, and the temperature variables are defined for Equation 6.12. Empirical degree-day factors range from 2 to 6 mm day-1 °C-1depending on specific site characteristics (Seidel and Martinec, 2004). Rango and Martinec (1995) suggest gradually increasing the degree-day factor over the course of the snowmelt season, and this approach is incorporated in the

widely used Snowmelt Runoff Model (Seidel and Martinec, 2004). The degree-day method is the standard tool for estimating snowmelt runoff, and the accuracy of this method is comparable to more complex energy balance formulations (Rango and Martinec, 1995). Clark and Vrugt (2006) successfully employ a two-parameter snow model using physically realistic parameterized temperature to estimate snow accumulation and melt in an alpine setting. The WMO (1986a) comparison of 11 snowmelt runoff models illustrates the capabilities of different modeling approaches.

6.11.4 Snowmelt runoff

It is difficult to quantify the fraction of runoff derived from snowmelt due to a lack of detailed knowledge of the runoff process. However, a smaller proportion of snowfall than of rainfall is evaporated and transpired, so it is clear that snowfall contributes proportionally more to runoff for those areas that receive a seasonal snowpack. It has been suggested that more than half the annual runoff in much of the Northern Hemisphere is derived from snowmelt, and the timing of winter-spring streamflow is important in these regions (Hodgkins and Dudley, 2006).

In considering snowmelt calculation for hydroclimatology, it is important to realize that all parts of a watershed may not have a snowpack or an evenly distributed snowpack. Temperature, wind, topography, and vegetation all influence the space and time variability of snow accumulation and ablation. Hill slopes in particular may contain mixed surfaces of snow, bare ground, and vegetation (Marks and Winstral, 2001; Pomeroy et al., 2003). However, Anderton et al. (2004) conclude that topographic controls on the redistribution of snow by wind are the most important influence on snow distribution at the start of the melt season because the spatial variability of melt is largely determined by the snow distribution rather than the spatial variability of melt rates. This means that the contributing area for snowmelt may be very different from the area responsible for rain-related runoff in a specific watershed. At the same time, the snowmelt runoff process is very different for high-elevation watersheds with a continuous snowcover relative to lower-elevation watersheds that have a snowpack on only a portion of their total area. A final complication is that while snow accumulates by elevation, snow melts by slope aspect. In the Northern Hemisphere, snowmelt on south-facing slopes occurs more rapidly than on valley-bottom sites or on north-facing slopes in response to energy balance differences (Pomeroy et al. 2003). These distinctions are important for snowmelt forecasting.

Meltwater is removed from the snowpack by gravity drainage. Since the majority of the melting occurs near the snow surface in response to available energy, there is a distinct daily rhythm to the production of meltwater in response to solar radiation. After being produced, the meltwater percolates through the snowpack. Consequently, there is a series of delays beginning with the transport of meltwater through the snowpack that produce a distinct lag in meltwater delivery to the stream channel (Meier, 1990).

Water arriving at the bottom of the snowpack either infiltrates into the soil or accumulates to form a saturated zone at the base of the snowpack. If the ground under the snowpack is not frozen or saturated, water percolating out of the base of the snowpack can infiltrate into the soil in the same manner as rainfall. However, snowmelt releases large quantities of water more slowly than the rate occurring in most flood-producing rainstorms, and the probability of the infiltration capacity being exceeded is low. In this case, the snowmelt water moves to the stream channel by the subsurface processes of throughflow or groundwater flow. The lag time for water reaching an upland stream channel is determined by the time required for vertical percolation in the snowpack and the travel time through the subsurface processes.

When the ground beneath the snowpack is frozen or saturated, infiltration into the soil is impeded and water percolating through the snowpack accumulates at the base of the snowpack. A saturated zone forms in the snowpack, and water moves downslope within the snowpack and just above the ground surface. When this is the dominant process, a wave of melt water arrives at the saturation zone in response to the daily energy balance, and the input wave produces a daily output wave that travels downslope in the basal saturated zone (Dingman, 1994). The lag time associated with this process is determined by the time required for water to percolate vertically through the snowpack. On slopes steep enough to promote drainage, the net storage effect of water draining through the snowpack is about 3 to 4 hours for moderately deep and fully ripened snow. In a shallow snow, the saturated zone may include the entire snowpack and create a slush layer with a liquid content almost great enough to promote downslope flow. The original structure of the snowpack is the basic impediment to flow by the complete layer (Meier, 1990).

The snowpack storage effect is the primary factor in regulating the volume and time distribution of snowmelt runoff. The physical properties of the snow-pack continue to change from the time of deposition to melt, and the storage effect is closely related to the snowpack energy balance. After melt occurs, watershed physical characteristics become a factor in the delivery of the meltwater to the stream channel. Small headwaters streams display the daily rhythm of the melt process with relatively short delays determined by the route the water takes in reaching the channel. After a week or more of active melt, the result is a peak flow by mid-afternoon followed by a rapid recession in the

Month

Fig. 6.10. Average monthly streamflow (1971-2000) for the Merced River at Pohono Bridge near Yosemite, California (38° N, elevation 1170 m), and average monthly precipitation (1971-2000) for Yosemite National Park, California, showing the contrasting seasonal regimes resulting from snow accumulation and melt. Shaded columns are precipitation, and the line is streamflow. (Streamflow data courtesy of the U.S. Geological Survey from their website at http://waterdata.usgs.gov/nwis/. Precipitation data courtesy of NOAA's National Climate Data Center and the Oak Ridge National Laboratory, Carbon Dioxide Information Analysis Center from their website at http://cdiac.ornl.gov/epubs/ndp/ushcn/usa_monthly.html.)

Month

Fig. 6.10. Average monthly streamflow (1971-2000) for the Merced River at Pohono Bridge near Yosemite, California (38° N, elevation 1170 m), and average monthly precipitation (1971-2000) for Yosemite National Park, California, showing the contrasting seasonal regimes resulting from snow accumulation and melt. Shaded columns are precipitation, and the line is streamflow. (Streamflow data courtesy of the U.S. Geological Survey from their website at http://waterdata.usgs.gov/nwis/. Precipitation data courtesy of NOAA's National Climate Data Center and the Oak Ridge National Laboratory, Carbon Dioxide Information Analysis Center from their website at http://cdiac.ornl.gov/epubs/ndp/ushcn/usa_monthly.html.)

evening as temperatures fall below freezing. This daily peak and recession pattern recurs for the remainder of the melt season (U.S. Army Corps of Engineers, 1956). In larger watersheds, the melt process begins at the lower elevations and proceeds to successively higher elevations. As an increasingly larger proportion of the watershed participates in the runoff process, the daily melt sequence becomes masked by runoff contributions from other storages. For example, in forested watersheds there is no basin-wide surface runoff from snowmelt. Practically all snowmelt runoff enters the stream channel as subsurface flow, groundwater flow, or a combination of both (Seidel and Martinec, 2004). At this spatial scale, the snowmelt influence becomes more apparent in monthly flows that increase to a peak in late spring or early summer when active snowmelt and all of the other storages are contributing to streamflow.

The seasonal snowpack effect on the annual distribution of runoff is illustrated by the Merced River (Fig. 6.10) which drains 831km2 surrounding Yosemite Valley in California. This watershed on the western slopes of the Sierra Nevada receives 114 cm of average annual precipitation, 96% of the watershed area is above the annual snowline, and average annual runoff is 64 cm (Rantz, 1972). The snowmelt influence on runoff is evident in the abrupt increase in April runoff, which is two months after the February precipitation maximum. May and June runoff accounts for nearly 60% of the annual total, but

Fig. 6.11. Daily streamflow (solid line) for the Merced River at Pohono Bridge near Yosemite, California (38° N, elevation 1170 m), and daily maximum air temperature (broken line) for Yosemite National Park, California, for 15 March 2002 to 15 July 2002. The streamflow response to increasing and decreasing temperature is an implied link with snowmelt. (Streamflow data courtesy of the U.S. Geological Survey from their website at http://waterdata.usgs.gov/nwis/. Temperature data courtesy of NOAA's National Climate Data Center and the Oak Ridge National Laboratory, Carbon Dioxide Information Analysis Center from their website at http://cdiac.ornl.gov/epubs/ndp/ ushcn/usa_daily.html.)

Fig. 6.11. Daily streamflow (solid line) for the Merced River at Pohono Bridge near Yosemite, California (38° N, elevation 1170 m), and daily maximum air temperature (broken line) for Yosemite National Park, California, for 15 March 2002 to 15 July 2002. The streamflow response to increasing and decreasing temperature is an implied link with snowmelt. (Streamflow data courtesy of the U.S. Geological Survey from their website at http://waterdata.usgs.gov/nwis/. Temperature data courtesy of NOAA's National Climate Data Center and the Oak Ridge National Laboratory, Carbon Dioxide Information Analysis Center from their website at http://cdiac.ornl.gov/epubs/ndp/ ushcn/usa_daily.html.)

May and June precipitation is only 6% of annual amount. November through March accounts for 76% of annual precipitation and most occurs as snow that remains until the height of the snowmelt season in May and June.

Figure 6.11 shows the daily streamflow response to snowmelt for the Merced River during the 2002 melt season. The daily maximum air temperature at a nearby station is included as a general indicator of energy available to drive snowmelt (Seidel and Martinec, 2004). The mean daily streamflow follows the increasing and decreasing daily maximum temperature with a lag that persists until after 1 June when most snowmelt has occurred. It is notable that the three peak flows are each preceded by several days of gradually increasing flows, and the greatest difference in the three events is 7 m3 s_1.

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