The aim of this assignment is to examine relationships between climatic variables and flow of rivers draining from glacierised basins in the Swiss Alps. The use of statistics will strengthen argument through highlighting significance between data. For this assignment you are to produce a word-processed document in the form of an essay. The essay should follow the structure given below and be no more than 1000 words.
The data used for this assignment is shown in table 1 and consist of thirty annual values, and have been explored previously in this module.
Table 1. Swiss Alps data for assignment 2. The five columns are year (A), May-September mean air temperature in degrees Celsius at Grächen (B), annual totals of river flow (discharge) in the Massa, which drains from Grosser Aletschgletscher, measured at Blatten-bei-Naters, for the same months ( x 106 m3 ) (C), annual totals of river flow in the Gornera, which drains from Gornergletscher, measured 0.75 km from the glacier terminus, for the months June through September( x 106 m3 )(D), and annual totals of precipitation (mm) between October (year-1) through May of the given year at Grächen (E), often called P10-5.
A B C D E
1970 10.81 379.05 92.157 315.9
1971 11.26 384.50 109.199 345.3
1972 9.60 289.14 83.593 353.0
1973 11.61 394.34 112.836 250.3
1974 10.52 316.13 100.054 223.3
1975 10.93 334.60 90.109 428.2
1976 11.13 338.28 96.043 282.7
1977 9.82 309.62 88.940 674.3
1978 9.86 274.30 71.732 572.6
1979 10.78 350.43 106.002 359.9
1980 10.08 295.73 92.290 557.1
1981 10.70 356.87 111.712 500.1
1982 11.96 430.89 134.233 412.4
1983 12.03 395.31 127.010 452.2
1984 9.77 285.13 99.103 398.3
1985 11.57 358.70 117.960 421.2
1986 11.99 389.51 128.608 527.7
1987 11.26 377.14 130.581 316.9
1988 11.68 397.56 127.674 444.4
1989 11.82 395.39 122.730 517.7
1990 12.26 427.23 134.898 293.7
1991 11.99 424.86 145.966 414.7
1992 12.43 441.08 127.092 329.3
1993 11.71 393.64 124.527 433.0
1994 12.54 496.27 158.297 430.5
1995 11.11 336.93 116.922 539.5
1996 11.13 320.18 105.320 233.2
1997 12.27 366.86 130.174 330.6
1998 12.85 423.32 148.544 258.3
1999 12.93 478.38 134.303 531.5
Both of the glaciers are in tributary valleys of the upper Rhone basin in Kanton Wallis, Switzerland hence are likely to have had very much the same pattern of climatic events over the 30-year period. Hence runoff from the two basins is likely to be strongly correlated.
Structure and contents of assignment.
(1) Write a brief introduction to the study areas, data etc. (given in table 1), maybe input an annotated map of location?
(2) Plot the time series of the flows of the two rivers on the same graph, and comment on the pattern of variation shown.
(3) Plot the two river flow series against each other as an xy scattergram. Comment on the distribution.
(4). Plot the histogram of annual total discharge of the Massa, using all the years. Comment on the dispersion shown. To what extent can annual discharge be considered to be normally-distributed?
(5) Calculate the Pearson’s product moment correlation coefficient between the two series. [Choose an empty cell on the spreadsheet – say G1 – and click there. In the text bar type = and then select CORREL from the drop down menu. Correlation coefficients are usually reported to two decimal places. Format cell, number, decimal places 2, enter].
How well are the two series correlated? Are there any periods when the series are not moving in tandem?
(6) Summer discharge from glacierised basins is likely to fairly strongly influenced by energy availability for melting snow and ice. Plot the xy scattergrams and calculate the correlation coefficients between air temperature and each of the discharge series. Why are both of these values less than 1.0? Add air temperature to the time series graph and add any further comments.
(7) Winter precipitation might affect runoff in summer in two opposing tendencies. In summers following winters with higher than average amounts of snowfall, then runoff might be expected to be enhanced as the additional snow is melted and contributes to runoff. Alternatively, high levels of winter snowfall may retard the rising of the transient snowline, especially when a snowy winter is followed by a cool spring. Such accumulation of snow will reduce the amount of ice melted in summer and hence tend to limit the amount of meltwater entering the discharge. Calculate the correlation coefficients between winter precipitation and each of the discharge series. Plot the xy scattergrams. Why are both of these values fairly close to 0.0? Why are the correlation coefficients negative?
(8) Are snowy winters followed by cool summers?
(9) By now sufficient correlation coefficients should have been calculated to produce a matrix of correlation coefficients between all the possible pairs of variables, as below:
Q5-9 Massa Q6-9 Gornera T5-9 Graechen
Q5-9 Massa – – –
Q6-9 Gornera – –
T5-9 Graechen –
P10-5 Graechen
Why are some cells excluded (-)? Complete the table and insert into the document.
(10) Add regression to the graphs produced.
(11) What does the r2 value describe?
(12) Is the regression line significantly different from one with gradient b=0 ?
The assignment should be written in the third person (no I did this, or we did that). It should be referenced to back up statements made and should be written as a logical essay structured based on the numbers (questions) above.
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