Table of Contents

1. Ex1 evaluate/plot bivariate Gaussian PDF
2. Ex2 analyse sea level pressure (SLP) anomalies
3. Procedure
4. Usage

Ex1

TASK: evaluate/plot bivariate Gaussian PDF

FILE: ex1/ex1_part_1.py

Input: 2 mean values, 2 variances, correlation parameter.

• PDF class calculates bivariate Gaussian PDF values at each location in the 2D grid.
• Create covariances 2x2 covariance matrix using input variances and covariances, calculated using correlation parameter
• create mehsgrid to be filled with PDF values
• calculate PDF value for each meshgrid cell using Gaussian PDF equation in matrix form
• plot PDF

FILE: ex1/ex1_part_2.py

Input: 2 mean values, 2 variances, correlation parameter, sample size of RV -m.

• Create covariances 2x2 covariance matrix using input variances and covariances, calculated using correlation parameter
• Get eigenvalues, eigenvectors of covariance matrix
• Get 2 × m matrix A, drawing m random samples from a normal (Gaussian) distribution
• Generate matrix Mu , containing two arrays of mean values of shape corresponding to size of arrays of independent random samples (m x m)
• Get X (2 x m) as X=np.dot(E,A)+Mu
• plot generated PDF for different correlation parameters

Ex2

TASK: analyse sea level pressure (SLP) anomalies

FILE: ex2/ex2_part1_Gordeev.py

Input: HadSLP2 netcdf, 2 variances, correlation parameter.

• Extract December months from netcdf file using xarray, plot the longterm mean SLP field for December
• Extract SLP time series from Reykjavik/Lisbon grid cells
• Plot 2D histogram with Reykjavik/Lisbon time series SLP data on x and y axis
• calulate bivariate normal distribution parameters(mean, variance and correlation) from Reykjavik/Lisbon time series
• generate and plot PDF with estimated parameters (same way as in Ex1)