Johnna_Assignment_1

I am using 2 observational time series for my multiple variables, precipitation from CMAP, and SST from NCDC. I formatted the data using grads.
 * Formatting Data:**

For CMAP:
 * The area averages are shown below -**

For SST (NINO 3.4 area)

This code creates 2 time series, shown below - So now I basically have 2 lists of numbers. One for SE US precip and one for NINO 3.4 SSTs. I created two .nc files for each, and also put the values into an excel spreadsheet so I could quickly look at the data (this is just what I do for some reason, creature of habit I guess!)

For Precipitation (showing varied number of bins from 10 to 50, you don't HAVE to show all these, I am for the sake of completeness): For SST (showing varied number of bins from 10 to 50): 30 bins looks best to me in both cases.
 * Histogram**


 * Now PDF of both precip and sst:**

Variance is defined: Where mu is the mean of the data. Note that standard deviation (sigma) is the square root of the variance. Matlab defines skewness as: Matlab defines kurtosis as:
 * First 4 Moments:**
 * || **Precip** || **SST** ||
 * **mean** || -2.55E-16
 * This is according to mean(precipanom), grads gives similar answer using ave(precipanom,time=jan1982,time=dec2009) || -1.07E-14
 * Same here ||
 * **variance** || 0.8571 || 0.7878 ||
 * **skew** || 0.3479 || 0.2176 ||
 * **kurtosis** || 2.8421 || 2.9582 ||
 * Mean:** Showing average value of both datasets over entire time period.
 * Variance:** Measure of how far the numbers are spread out, how far the numbers lie from the mean.
 * Skewness:** Measure of asymmetry of the probability distribution. Negative skew means "tail" on left hand side of PDF is longer than right side, so the values are skewed to the left. Vice versa for positive. Zero skewness means that the values are evenly distributed on both sides of the mean (symmetric).
 * Kurtosis:** A measure of the "peakedness" of the probability distribution. In other words, it describes the shape of the probability distribution. High kurtosis means a sharp peak with long, fat tails. Low kurtosis means more rounded peak and short, thin tails.


 * Scatterhist(PrecipAnom,SSTAnom):**


 * Hist3:**
 * Normalized Hist3:**

Covariance of two variables is given by the formula:
 * Covariance:**

Covariance measures (in short) how much corresponding elements from two sets of data move in the same direction. Positive covariance means the two elemens move together, so the two things varied together in the same direction from their means. If covariance is negative, they varied in opposite directions. Larger magnitude of he product, the stronger the relationship. Positive covariance: Higer tan average values of 1 variable are paired with higher than average values of the other. Negative covariance: Higher than average values of one variable paired with lower than average values of the other variable. The cov(X,Y) function in matlab returns a covariance matrix. The matrix given by matlab shows the variance on the diagonal, and the covariance in the other numbers. cov(precipanom, sstanom)=

0.8571 0.1756

0.1756 0.7878

Notice that the diagonal (0.8571 and 0.7878) correspond to the values of precipitation variance and sst variance given in the table above. The other two values represent the covariance of precipitation and sst.

This is just to give you an example of something you could look at. The conditional sample could be anything from a peak, to a tail of your distribution, etc. For instance, I could use the right hand tail of the distribution of precipitation (values greater than 1ish), but you could pick something else - You can use something like find(variable>value) in matlab. Then compare that to some other available variables using the same conditional sample (so if your conditional sample involves month 1,3,5, your conditional sample of other variables should involve month 1,3,5).
 * Conditional Sample:**

This plot shows the right hand tail of the precipitation distribution (in the top left hand corner), as compared to the entire SST distribution (bottom right hand corner), so a little different than above, using the plotmatrix function in matlab:

For my research, I have specifically been looking at the 2006-2007 SE US drought. My "conditional sample" will involve the datapoints from those 2 years, beginning Jan2006 and ending dec2007 for both precip and SST. As expected, since this is a drought, the histogram for precipitation is negatively skewed. I computed the skewness as -0.5570, so the left hand tail is longer than right, and in this case the frequency is highest below 0. For SST, the skewness is -0.2127, so now for both variables there is negative skew as opposed to what was shown for the entire dataset.