ENNEC 472: Quantitative Analysis in Earth Sciences

Spring 2009

PROBSET #1 (DUE: Tu Feb 3 at start of class)

Discrete and Continuous Distributions

1. Analysis of Atlantic Tropical Cyclone Totals

We will use the statistical model of a “Poisson” process to analyze long-term Atlantic Tropical Cyclone data.

a. Download the Landfalling (Atlantic) U.S. Hurricanes annual totals from 1870-2006 (as with other time series, a two column format is used where the first column is the year, and the 2^nd column is the data value for that year)

b. Plot and compare the observed and theoretical calculated Poisson distributions. Comment on how well the observed distribution conforms to the theoretical expectations. You may make use of the Matlab subroutine “poissonfit.m” used in class, but you should understand what the routine is doing.

c. Plot the annual number of storms as a function of time. Plot a horizontal line that indicates the average yearly total (i.e., the long-term mean of the series)._

d. Use the estimated Poisson distribution to calculate the probability in any one season of randomly equaling or exceeding the observed total for the 2005 storm season, for which there were 5 landfalling Atlantic Hurricanes.

2. Analysis of Atlantic Tropical Cyclone Totals, Revisited

Repeat problem #1 but using instead the time series of Landfalling Atlantic Hurricanes during only (1) El Nino Years and (2) La Nina Years [for those who are interested, I produced these series by using the long-term December-February instrumental 'Nino3.4' series which measures relative variations in Sea Surface Temperatures (SSTs) in degrees C in the eastern equatorial Pacific, defining El Nino and La Nina years as corresponding to all winters where the values of the series are larger than 1, or more negative than -0.6, respectively. Note that the convention for the El Nino ‘year’ is the year corresponding to the January and February, rather than the December (i.e., the calendar year that follows the tropical storm season.]

Compare with the results from problem #1. Interpret and discuss.

3. Analysis of State College December monthly mean temperatures

We will use the statistical model of a “Gaussian” process to analyze long-term State College monthly temperature data.

You may make use of the Matlab subroutine “gaussian.m” used in class, but you should understand what the routine is doing [you will also need to download the subroutine “quantiles” which is required by “gaussian”]

a. Download the State College PA long-term December mean monthly surface temperature data (in ^oF) for 1888-1994.

b. Compare the observed and theoretical calculated Gaussian distributions. Comment on how well the observed distribution conforms to the theoretical expectations.

c. Now calculate the mean and standard deviation of the series. Plot the annual time series, and use three horizontal lines to indicate the mean and the expected 2.5% and 97.5% exceedance probability thresholds for a Gaussian distribution. How many events fall below and above these thresholds? Does this conform to your expectations?

d. The average temperature for State College for this past December was 32^oF. Using the information provided above, calculate the probability of randomly equaling or exceeding this value in a given year.

4. Analysis of Indian-Monsoon related Precipitation

Use the statistical model of a “Gaussian” process to analyze PA long-term Indian Monsoon-related precipitation data (in total mm accumulated during rainy season) for 1871-2000, repeating steps a-c of problem #3 for this time series.