The Relationships between Climate and River flow in the Alps

(1) Write a brief introduction to the study areas, data etc. (given in table 1), maybe input an annotated map of location?

The study is a presentation of statistical review of patterns in yearly flow records of the Swiss Alps for successive period of 30 years. The study sets out to determine various significant trends observed at various time series.

(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?

0.86909. Because the Pearson correlation value is greater than 5% at 0.869. The statistics fails to demonstrate a significant correlation between the two series.

(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?

The Correlation coefficient is -0.13788: This therefore demonstrates a strong and positive correlation between the discharge series because the Pearson’s Correlation value is less than 0.005 at -0.13788. Implicitly, winter precipitation has a bearing on the discharge.

(8) Are snowy winters followed by cool summers? Yes: Summers tend to be cool owing to the cloud cover while winters are milder beyond expectations because of the latitude.

(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

	Column 1	Column 2	Column 3	Column 4
Column 1	1
Column 2	0.90565	1
Column 3	0.886126	0.86909	1
Column 4	-0.20826	-0.11811	-0.13788	1

Why are some cells excluded (-)? Complete the table and insert into the document.

(10) Add regression to the graphs produced.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.989195

R Square

0.978507

Adjusted R Square

0.942793

Standard Error

296.1631

Observations

ANOVA

Significance F

Regression

1.12E+08

1274.761

2.91E-24

Residual

2455952

87712.58

Total

1.14E+08

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

#N/A

379.05

5.222358

0.146269

35.7038

6.78E-25

4.92274

5.521976

4.92274

5.521976

RESIDUAL OUTPUT

PROBABILITY OUTPUT

Observation

Predicted 1970

Residuals

Standard Residuals

Percentile

1970

2007.997

-36.9967

-0.12713

1.724138

1971

1509.993

462.0074

1.587589

5.172414

1972

2059.385

-86.3847

-0.29684

8.62069

1973

1650.944

323.0559

1.110112

12.06897

1974

1747.401

227.599

0.782095

15.51724

1975

1766.619

209.3807

0.719492

18.96552

1976

1616.947

360.0535

1.237246

22.41379

1977

1432.493

545.5072

1.874518

25.86207

1978

1830.071

148.9291

0.511763

29.31034

1979

1544.408

435.592

1.496818

32.75862

1980

1863.703

117.2971

0.403066

36.2069

1981

2250.262

-268.262

-0.92182

39.65517

1982

2064.45

-81.4504

-0.27989

43.10345

1983

1489.991

494.009

1.697555

46.55172

1984

1873.26

111.7402

0.383971

1985

2034.161

-48.1607

-0.16549

53.44828

1986

1969.56

17.43988

0.059928

56.89655

1987

2076.201

-88.2007

-0.30308

60.34483

1988

2064.868

-75.8682

-0.2607

63.7931

1989

2231.148

-241.148

-0.82865

67.24138

1990

2218.771

-227.771

-0.78269

70.68966

1991

2303.478

-311.478

-1.07033

74.13793

1992

2055.729

-62.729

-0.21555

77.58621

1993

2591.7

-597.7

-2.05387

81.03448

1994

1759.569

235.4309

0.809007

84.48276

1995

1672.095

323.9054

1.113031

87.93103

1996

1915.874

81.12572

0.278771

91.37931

1997

2210.259

-212.259

-0.72938

94.82759

1998

2498.272

-499.272

-1.71564

98.27586

1999

(11) What does the r2 value describe?

The Regression model explains 97.85 percent of the variation of the time series

(12) Is the regression line significantly different from one with gradient b=0 ?

Yes: The statistics shows that the slope is significantly different from zero,

The observed data indicate that the slope is significantly different from zero, thus observed statistics positively indicate that precipitation are largely dependant on various environmental factors

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