## Relationships between climate and river flow in the Alps

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

– which includes all words except references.

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 E1970 10.81 379.05 92.157 315.91971 11.26 384.50 109.199 345.31972 9.60 289.14 83.593 353.01973 11.61 394.34 112.836 250.31974 10.52 316.13 100.054 223.31975 10.93 334.60 90.109 428.21976 11.13 338.28 96.043 282.71977 9.82 309.62 88.940 674.31978 9.86 274.30 71.732 572.61979 10.78 350.43 106.002 359.91980 10.08 295.73 92.290 557.11981 10.70 356.87 111.712 500.11982 11.96 430.89 134.233 412.41983 12.03 395.31 127.010 452.21984 9.77 285.13 99.103 398.31985 11.57 358.70 117.960 421.21986 11.99 389.51 128.608 527.71987 11.26 377.14 130.581 316.91988 11.68 397.56 127.674 444.41989 11.82 395.39 122.730 517.71990 12.26 427.23 134.898 293.71991 11.99 424.86 145.966 414.71992 12.43 441.08 127.092 329.31993 11.71 393.64 124.527 433.01994 12.54 496.27 158.297 430.51995 11.11 336.93 116.922 539.51996 11.13 320.18 105.320 233.21997 12.27 366.86 130.174 330.61998 12.85 423.32 148.544 258.31999 12.93 478.38 134.303 531.5

write the assignment as an essay, with the structure as below.

(1) A brief introduction to the study areas, data etc. (given in table 1), it is usual that an annotated map of location is presented.

(2) Plot the discharge time series of the two rivers on the same graph, and comment on the pattern of variation shown.

(3) Plot the two river flow series directly against each other as an xy scatter plot. Comment on the distribution.

(4). Plot an appropriate histograms of annual total discharge, using all the years. Comment on the dispersion shown. To what extent can annual discharge be considered to be normally-distributed?

How do the histograms compare between rivers.

(5) Calculate the Pearson’s product moment correlation coefficient between the two series. [Use the CORREL function from the drop down menu. Correlation coefficients are usually reported to two

decimal places.

How well are the two series correlated? Are there any periods when the series are not moving in tandem? What possible reasons could there be for this?

(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 then discuss, adding

further comments when required.

(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) Given the data processed thus far, 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

This matrix can easily be completed using the data analysis tab & ‘correlation’. Why are some cells excluded (e.g. -)? Complete the table/undertake the correlation data analysis and insert into

the assignment document.

(10) Add regression to the graphs produced.

(11) What does the r2 value describe? Comment on the spread of data and what the findings may mean.

(12) Is the regression line significant?

(13) Draw final conclusions from the work

(14) Include your reference list.