QUESTIONS

  1. What atmospheric and environmental conditions control snow accumulation?

    Snow accumulation is a function of the following atmospheric and environmental conditions: (1) surface air temperature, (2) elevation, (3) slope and aspect of terrain, (4) wind, (5) energy and moisture transfer, and (6) vegetative cover.

  2. What is albedo? What is a typical range of albedo for snow-covered surfaces?

    Albedo is the ratio of reflected to incident shortwave radiation.

    Typical values of albedo for different snow-covered surfaces vary from 0.8 for exposed surfaces to 0.12 under extensive coniferous forest cover.

  3. What are the principal sources of heat energy involved in melting of the snowpack?

    The principal sources of heat energy involved in the melting of the snowpack are: (1) net shortwave (i.e., solar) radiation, (2) net longwave (i.e., terrestrial) radiation, (3) convective heat transfer from atmosphere to snowpack, (4) heat transfer caused by condensation of water vapor onto snowpack, (5) heat transfer from rainwater to snowpack, and (6) heat conduction from underlying ground to snowpack.

  4. What is the thermal quality of a snowpack? What is a typical value of thermal quality for a ripe snowpack?

    Thermal quality is the ratio of the heat necessary to produce a given amount of water from the snowpack to the heat necessary to produce the same amount of water from pure ice, expressed as a percentage.

    A typical value of thermal quality for a ripe snowpack is 97 percent.

  5. What is the solar constant? What is the value of the solar constant?

    The solar constant is the intensity of solar radiation received on a unit area of a plane normal to the incident radiation at the outer limit of the earth's atmosphere, with the earth at its mean distance from the sun.

    The value of the solar constant is generally taken to be 1.94 langleys per minute, although variations in the range 1.94-2.0 langleys per minute have been reported.

  6. What is insolation? What is the value of daily insolation amount received at the outer limit of the earth's atmosphere for a 30°N latitude at winter solstice?

    Insolation is the amount of shortwave (i.e., solar) radiation incident on a horizontal surface.

    From Fig. 12-1, the daily insolation received at the outer limit of the earth's atmosphere for a 30°N latitude at winter solstice is 470 langleys.

  7. What is convective melt? What is condensation melt?

    Convective melt is the snowmelt caused by convective heat transfer from atmosphere to snowpack.

    Condensation melt is the snowmelt caused by condensation of water vapor onto snowpack.

  8. What is rain melt? What is ground melt?

    Rain melt is the snowmelt caused by heat transfer from rainwater to the snowpack.

    Groundmelt is the snowmelt caused by heat conduction from the ground to the snowpack.

  9. What are the controlling factors in shortwave radiation melt?

    The controlling factors in shortwave radiation melt are: (I) shortwave radiation amount; (2) albedo of the snow surface, (3) thermal quality of the snowpack.

  10. What is an index in hydrologic practice?

    In hydrologic practice, an index is a readily measured meteorologic or hydrologic variable that is related to a physical process in need of monitoring and whose variability can be used as a measure of the variability of the physical process.

  11. What is the controlling factor for snowmelt runoff from an open site? What are the most important components in snowmelt runoff from forested areas?

    All-wave radiation is the controlling factor for snowmelt runoff from an open site.

    Convection and condensation melt are the most important components in snowmelt runoff from forested areas.

  12. What is a degree-day? What is the degree-day factor?

    A degree-day is an index used to measure snowmelt runoff. For any day for which the temperature is above a temperature base (usually the freezing level), the number of degree-days is the difference between the actual temperature and the temperature base.

    The degree-day factor is a unit melt rate defined as the number of centimeters or inches of melt per degree-day.

  13. What is ripening of the snowpack?

    Ripening is the process by which a snowpack changes from a loose, subfreezing, low-density state to a coarse, granular, moist, high-density state.

  14. How many types of water exist in the snowpack? Explain.

    Water exists in the snowpack in three forms:

    (1) Hygroscopic water, which is adsorbed as a thin film on the surfaces of snow crystals and is unavailable for runoff until the snow crystals have melted or changed in form;

    (2) Capillary water, held by surface tension in the capillary spaces around the snow particles, free to move under the influence of capillary forces but unavailable for runoff until the snow melts or the spacing between snow crystals change; and

    (3) Gravitational water, in transit through the snowpack under the influence of gravity, draining freely from the snowpack, and available for runoff.

  15. Describe the elevation-band method for determining spring snowmelt runoff hydrographs.

    The basin is subdivided into several elevation bands, and snowmelt, rainfall and losses (hydrologic abstractions) are computed for each band. Melt and rain are assumed to be spatially uniform throughout each band, and the entire band is assumed to be either snow-covered or snow-free and melting or not melting. Snowmelt is computed by using temperature or other appropriate indexes. Excess basin water available for runoff is obtained by weighing rainfall, snowmelt, and losses in proportion to the individual band subareas.

PROBLEMS

  1. Calculate the daily snowmelt rate for a snowpack of 95% thermal quality subject to a snowmelt heat equivalent of 570 ly/d.

    Using Eq. 12-2, the daily snowmelt rate is:

    M = (1.25 × 570 ly/d) / (95%) = 7.5 cm/d.  ANSWER.

  2. Calculate the shortwave radiation snowmelt for a snow-covered site with insolation under clear sky 590 ly/d, cloud cover coefficient 0.8, forest transmission coefficient 0.9, snow surface albedo 0.7, and thermal quality of the snowpack 97%.

    Using Eq. 12-8, with corrections to insolation by Eqs. 12-4 and 12-6, the net shortwave radiation is:

    Hs = 590 ly/day × 0.8 × 0.9 × (1 - 0.7) = 127.44 ly/d

    Using Eq. 12-7, the shortwave radiation snowmelt is:

    Ms = (1.25 × 127.44 ly/d) / (97%) = 1.64 cm/d.  ANSWER.

  3. The following mean daily temperatures (in degrees Celsius) were measured in a snowcovered forest site during a certain week: Monday, 10°C; Tuesday, 11°C; Wednesday, °C;Thursday, 13°C; Friday, 12°C; Saturday, 14°C, and Sunday, 11°C. Calculate the melt for a degree-day factor of 0.25 cm/(°C;-d). Assume a temperature base of O°C.

    The total number of degree-days is: 83 °C-d. Therefore, the melt is:

    M = 0.25 cm/(°C-d) × 83 °C-d = 20.75 cm.  ANSWER.

  4. The following mean monthly temperatures have been recorded in a snow-covered forest site during the spring: April, 44°F; May, 52°F; and June, 60°F. The snowpack water equivalent at the end of March is 36 in. Assuming a degree-day factor of 0.04 in./(0°F-d), determine the potential snowmelt during the 3-month period. Compare this potential snowmelt value with the water equivalent at the end of the snowfall season (assume end of March) to determine whether there is any melt in Mayor June. Assume a temperature base of 32°F.

    The total number of degree-days during the three-month period is:

    [(44 - 32) × 30 + (52 - 32) × 31 + (60 - 32) × 30] = 1820 °F-d.

    The potential snowmelt is:

    M = [0.04 in/(°F-d)] × 1820 °F-d = 72.8 in.  ANSWER.

    The April melt is: M = [0.04 in/(°F-d)] × [(12 × 30) °F-d] = 14.4 in, which is less than the available snowpack water equivalent (36 in)

    The May melt is: M = [0.04 in/(°F-d)] × [(20 × 31) °F-d] = 24.8 in

    The combined April and May melt is: M = 39.2 in, which exceeds the available snowpack water equivalent. Therefore, there is no melt during the month ofJune.  ANSWER.

  5. Compute basin snowmelt using a generalized snowmelt equation for the following data: forested area; wind speed at 50-ft above the snow surface, v = 30 mph; air temperature at a 10-ft height, 65°F; dew point temperature at 10 ft height, 50°F; snow surface temperature, 32°F; and basin factor k = 0.4.

    Using Eq. 12-16b, the basin snowmelt is:

    M = 0.4 × (0.0084 × 30) [(0.22 × 33) + 0.78 × 18)] + (0.029 × 33)

    M = 3.104 in/d.  ANSWER.

  6. Compute basin snowmelt using a generalized snowmelt equation applicable for rainfall periods for the following data: heavily forested area; temperature of saturated air at a 10-ft height, Ta = 60°F; and rainfall rate Pr = 1.5 in./d.

    Using Eq. 12-17b, the basin snowmelt is:

    M = (0.074 + 0.007 × 1.5) × (60 - 32) + 0.05 = 2.416 in/d. ANSWER.

  7. Given the following area-elevation data and daily rainfall, snowmelt, and losses for a certain basin, use the elevation-band method to compute the excess basin water available for runoff.

    Elevation
    Band (m)    		 Subarea
    (km2)    		 Rainfall
    (cm/d)    		 Snowmelt
    (cm/d)    		 Losses
    (cm/d)
    2000 - 2500 150 4 0 3
    2500 - 3000 100 5 4 2
    3000 - 3500 50 6 2 1

    Using Eq. 12-19, the excess basin water available for runoff is:

                    [(4 + 0 - 3) × 150] + [(5 + 4 - 2) × 100] + [(6 + 2 - 1) × 50]   
    Me =   _______________________________________________________________
                                                (150+100+50)

    Me = 4 cm.  ANSWER.

  8. Given the following area-elevation data for a certain basin, use the rational method to compute the excess basin water available for runoff. Assume snow line at elevation 2200 m; melt line at elevation 2600 m; mean basin rainfall, 7 cm/d; snowmelt, 3 cm/d; and mean basin losses, 2 cm/d.

    Elevation (m) 2000 2200 2400 2600 2800 3000
    Cumulative Area (km2) 0 450 630 730 800 840

    The total basin area is: A = 840 km2.

    The area contributing snowmelt Ac is the difference between the cumulative basin areas corresponding to melt line and snow line elevations.

    Then: Ac = 730 - 450 = 280 km2

    Therefore, the mean basin melt rate is:

    M̄ = M × (Ac /A) = 3 cm/d × (280 km2 / 840 km2) = 1 cm/d.

    The excess basin water available for runoff Me is:

    Me = P + M̄ - L = 7 + 1 - 2 = 6 cm/d.  ANSWER.

  9. Given the following area-elevation data for a certain basin, use the rational method to compute the excess basin water available for runoff. Assume snow line at elevation 5000 ft; melt line at elevation 6000 ft; mean basin rainfall, 2 in./d; mean basin losses, 0.5 in./d; degree-day factor 0.075 in./(0°-d); temperature at the index station at elevation 5500 ft, 42°F; and a temperature gradient of -10°F per 500-ft increase in elevation.

    Elevation (ft) 4500 5000 5500 6000 6500
    Cumulative Area (mi2) 0 500 900 1200 1400

    The total basin area is: A = 1400 mi2.

    The area contributing snowmelt At is the difference between the cumulative basin areas corresponding to melt line and snow line elevations.

    Then: Ac = 1200 - 500 = 700 mi2

    The calculations are summarized in the following table.

    Elevation

    (ft)    		 Area

    (mi2)    		 Area
    Increment
    (mi2)    		 Temperature

    (°F)    		 Average
    temperature
    (°F)    		 Degree-days
    4500 0 62
    500 57 25
    5000 500 52
    400 47 15
    5500 900 42
    300 37 5
    6000 1200 32
    200 27 0
    6500 1400 22

    The weighted melt between the elevations of 5000 ft (snow line) and 6000 ft (snow melt) is:

    Ms = [0.075 in/(°F-d)] × [(15 × 400) + (5 × 300)] / (700) = 0.8 in/d

    The mean basin melt rate is:

    M̄ = Ms × (Ac / A) = (0.8 in/d) × (700/1400) = 0.4 in/d.

    The excess basin water available for runoff is:

    Me = P + M̄ - L = 2.0 + 0.4 - 0.5 = 1.9 in/d.  ANSWER.

  10. Using Fig. 12-8, determine the mean basin melt rate for the Boise River Basin above Twin Springs, Idaho, for the following conditions: (a) mean air temperature of 55°F and snow line at elevation 5500 ft; and (b) mean air temperature of 65°F and snow line at elevation 7000 ft.

    Using Fig. 12-8, the mean basin melt rate for the Boise River Basin above Twin Springs, Idaho, is:

    (a) 0.74 in/d.  ANSWER.

    (b) 0.54 in/d.  ANSWER.

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