ENNEC 472: Quantitative Analysis in Earth Sciences

Spring 2009

PROBSET #3 (DUE: Tu Apr 7 at start of class)

Linear Regression and Trend Analysis

1. Estimation of Linear Trends

For each of the following time series, determine whether or not there is a statistically significant trend, and plot the estimated trend along with actual series.

a. State College December Temperatures (1888-1994)

b. Atlantic Annual Named Tropical Storm totals (1870-2008)

c. Annual Global Mean Surface Temperatures (1850-2008) [note: 1^st column is year, 14^th column is annual mean, you can ignore all other columns]

d. Asian Summer Monsoon-related precipitation (1871-2000)

In each case, if a statistically significant trend is found, you should plot the raw data along with a time series that reflects the statistical model for the trend in the data.

Be clear about what significance thresholds you’ve chosen, and in each case explain whether you have invoked a one-sided or two-sided hypothesis test (and why). Discuss how confident you are with the results of the trend analysis, and why (hint: you should look at the residuals!).

2. Analysis of El Nino influences on Miscellaneous Weather and Climate Phenomena

We will analyze the same 4 series used in question #1:

a. State College December Temperatures

b. Atlantic annual Named Tropical Storm totals

c. Annual Global Mean Surface Temperatures

d. Asian Summer Monsoon-related Precipitation

However, we will now investigate a different question, namely whether there is a statistically significant relationship with El Nino in each of these 4 different cases.

We will use the boreal winter instrumental 'Nino3.4' series (1871-2006) as a measure of El Nino. Note that we can only make use of the common time interval during which both series (Nino3.4 and the series a-d being considered) are available in each analysis. Recall that the convention for the Nino3.4 series is that the ‘year’ corresponds to the January of the DJF average. So for example, the 1871 value represents winter 1870/1871. Keeping in mind this definition, makes comparison with series ‘c’ for the same year (i.e. 1871 value would be compared with 1871 Nino3.4 value), and with series ‘a’,‘b’, and ‘d’ for the preceding year (e.g. 1900 value would be compared with 1901 Nino3.4 value).

In each case, if a statistically significant relationship with El Nino is found, you should plot the raw data along with a time series that reflects the statistical model for the component of the data that is attributed to El Nino influences.

As with problem #1, be clear about what significance thresholds you’ve chosen, and in each case explain whether you have invoked a one-sided or two-sided hypothesis test (and why). Discuss how confident you are with the results of the regression analysis, and why (see hint in problem #1 above).