SNOW HYDROLOGY (GEOG 4321): HOMEWORK ASSIGNMENT 3

Instuctor: Mark Williams
Telephone: 492-8830

Homework 3

• Assigned 7 February.
• Due 11 February, 4 PM to Craig's mailbox at Guggenheim.
• There are 40 possible points, each question is worth 8 points.
• SHOW ALL YOUR WORK.
• WRITE NEATLY and LEGIBLY.
• WRITE THE QUESTION AT THE START OF EACH ANSWER.

1. Mountain snowpacks are best characterized by digging snowpits in order to measure changes in physical properties of the snowpack (temp, density, stratigraphy...) with depth. For the next two questions, you will compare data collected from pits 006 and T3E on 14 March 1995. Pit 006 is a snow pit at a natural site on the saddle of Niwot Ridge. Pit T3E is behind a snowfence, only 50 m from pit 006. The snowfence is part of a long-term experiment to look at the effects of increased snow deposition on the biology and chemistry of an alpine tundra ecosystem. Please show all of the work for your answers. To find the data, go to http://culter.colorado.edu/, enter the new site, under Data select available data, then Hydrology, then Niwot Ridge/Green Lakes Valley snow cover profiles: Raw data.
• Calculate the depth-weighted mean density for each of the pits.
• Calculate the depth-weighted mean temperature for each of the pits.
• Calculate the total snow water equivalence for each of the pits.
• note: the first and last rows of data for each snowpit contain only the temperature at the snow/soil interface and at the snow surface respectively.
2. For the same snowpits (006 and T3E on 14 March 1995), graph a temperature profile and graph a density profile. The x-axis is either temperature or density, increasing from left to right. The y-axis is snow depth in meters, with 0 (the soil) at the bottom of the y-axis and the top of the y-axis is the top of the snowpack. Density is the column "measured weight"; units are grams/1000ml, which is the same as kg/m3. Temperature is the column "measured temperature".
• Graph temperature from the two pits on the same graph.
• Graph density from the two pits together on another graph.
• In ten sentences or less, explain why the two pits have different density and temperature values.
3. Wind during snow events generally causes precipitation gauges to undercollect the "true" snowfall amount. The Niwot Ridge saddle area during the winter months is characterized by average wind speeds of about 10-13 m/s. Further up Niwot Ridge, the D1 meteorological site has much lower wind speeds. Compare the annual precipitation amounts from Sdl and D1 to see if they do in fact collect significantly different amounts of annual precipitation.

Year    Saddle  D1
(year)  (mm)    (mm)
----    ----    ----
1986    1117    0908
1987    1790    1271
1988    1497    1055
1989    1827    1074
1990    1877    1037
1991    1269    1213
1992    1985    1502
1993    1544    1159
1994    2683    1568
1995    2955    1231

• Graph an XY scatter plot of Saddle (dependent variable) versus D1 (independent) annual precipitation.
• Regress Sdl ppt on D1 ppt using a linear relationship. Include the line equation and r2 values on the graph. Is there a significant relationship between precipitation measurements at the two sites on an annual timescale?
• Test to see if annual Sdl ppt is significantly different than D1 ppt using a paired t-test (the default on Excel)
4. Following is a small data set on wind speed and catch ratio of snowfall from Niwot Ridge. Graph wind speed (x axis) versus catch ratio on the y-axis. Explain these results in 5 sentences or less.

Wind    Catch
Speed   Ratio
(m/s)   (fraction)
----    ----
1.6     1.00
1.75    0.91
2.5     0.59
2.7     0.58
8.2     1.23

5. The precipitation amount measured by a precipitation gauge can be adjusted for blowing snow using the following equations:

        Pa = K * Pg
                Pa = adjusted precipitation
                Pg = gauge-measured precipitation
                 K = 1/CR, adjustment factor for wind-induced error
                CR = catch ratio of the gauge
                CR = alter shield and snow = exp (0.0055-0.133Ws)
                CR = no shield and snow = exp (-0.251-0.176Ws)
                Ws = Wind speed (m/s) at gauge opening 
                CR = HAS NO UNITS, SINCE WE ARE CALCULATING A RATIO
                note: exp(x) = ex

• Assume 50 mm of precipitation for the following questions:
• What is Pa for Ws = 0; alter shield and snow?
• What is Pa for Ws = 2; alter shield and snow?
• What is Pa for Ws = 10; alter shield and snow?
• What is Pa for Ws = 10; no alter shield and snow?
6. Extra Credit (5 points). Graph a density profile from the middle pit from Saturday's field trip, using both methods. Which method has more "error". Calculate the coefficient of variation for the two methods. Explain why the two methods do not always provide the same density value for the same layer.