WAMI is the acronym for Wavelet Analysis of Magnetosphere and Ionosphere, a research project funded by NSF award DMS-0413653 Statistical Wavelet Analysis and Indices Development of the Magnetosphere-Ionosphere Current System Observed by the Terrestrial Magnetometers (mathematical geosciences). Currents flowing in the magnetosphere-ionosphere (M-I) form a complex multiscale system in which a number of individual currents connect and influence each other. The variabilities of these currents are closely connected to various nonlinear dynamic M-I processes, such as magnetic storms and substorms, driven by the solar energy, Fig 1.

Among the various observational means, the global network of ground-based magnetometers stands out with unique strengths of global spacial coverage at all time scales. About a hundred terrestrial geomagnetic observatories form a network, INTERMAGNET, designed to monitor the variations of the M-I current system. Modern digital magnetometers record three components of the magnetic field in five second resolution, but the INTERMAGNET's data we use consist of one minute averages, i.e. 1440 data points per day per component per observatory.

An example of a one day long magnetometer record is shown in Fig. 2. It shows a signature of an event known as a substorm. Substorms occur over polar regions, and are associated with the Auroras.

The main focus of our research has been the development of a cleaner index of storm activity. We have done extensive work on deconvoluting the signature of the symmetric ring current, depicted in Fig. 4, which is the largest storm time feature. This is a difficult task because magnetometer records contain nonlinearly superimposed signatures of many currents. We developed new statistical techniques, based on wavelet and functional data analysis, that have brought us closer to this goal.

## WAMI Team

The team currently consists of three space physicists (Sojka, Zhu, Xu) and three statisticians (Gabrys, Kokoszka, Maslova).

### Physicists

Jan Sojka is Professor and Department Head in the Department of Physics and a member of the Center for Atmospheric and Space Sciences (CASS), a research unit of the College of Science. He is the president of the Space Science and Aeronomy Section of the American Geophysical Union. In 2005-2007, he chaired the National Science Foundation CEDAR Science Steering Committee. In 2002, he was selected as the Utah Professor of the Year by the Carnegie Foundation for the Advancement of Teaching. His research interest include many areas of ionospheric and magnetospheric physics.

Lie Zhu is Research Associate Professor in the Center for Atmospheric and Space Sciences. He served on NSF and NASA review panels. His research focuses on magnetospheric physics and M-I coupling.

Zhonghua Xu is a PhD student in the Department of Physics. He works on improving the statistical techniques resulting from the WAMI project to obtain precise insights into the structure of selected magnetospheric currents.

### Statisticians

Piotr Kokoszka is Professor in the Department of Mathematics and Statistics. He is an Associate Editor of the journal "Statistical Modelling". His research focuses on statistical modeling of nonstandard data sets exhibiting complex multiscale dependence and nonlinearities.

Agnieszka Jach received PhD in Statistics from Utah State University in 2005. She is now Assistant Professor in the Department of Statistics at Universidad Carlos III de Madrid Spain. Her research focuses on applications of wavelet and resampling methods.

Inga Maslowa received PhD in Statistics from Utah State University in 2009, and is now Assistant Professor in the Department of Mathematics at American University, DC. Her research has focused on applications of wavelet and functional data analysis to magnetometer data.

Robertas Gabrys is a PhD candidate in the Department of Mathematics and Statistics. He works on applications of the statistical techniques developed in the course of the WAMI project to data sets arising in climatology and finance.

## Publications

Selected publications generated by the WAMI project.

(Statistical methodology and applications to magnetogram data)

L. Horvath, M. Huskova and P. Kokoszka, Testing the stability of the functional autoregressive process, Journal of Multivariate Analysis, 00 , 000-000, 2008

## Presentations

Colloquium talk given by Piotr Kokoszka at UC Davis in April 2009

Talk given by Inga Maslova at Joint Assembly Spring 2008 meeting, Fort Lauderdale

Poster presented by Inga Maslova at AGU Fall 2007 meeting, San Francisco

Talk given by Piotr Kokoszka at an international conference in Graz in May 2007

Poster presented by Inga Maslova at JSM 2007 meeting, Salt Lake City

Poster presented by Inga Maslova at AGU Fall 2005 meeting, San Francisco

Poster presented by Agnieszka Jach at AGU Fall 2005 meeting, San Francisco

## Software

We present here the code for an R-package which will soon become available at the Comprehensive R Archive Network (CRAN). The code is now available from this site as a zip file Rpackage.zip. Please address any questions to inga.maslova@gmail.com

The main functions are "SAI" (in the file index.R) and "SQ.new".

The first one computes the storm activity index associated with the ring current. It is an automated procedure that requires the user to input the raw magnetometer data and the coordinates of the stations used. The second major function of this package, "SQ", computes the estimate of the Solar quiet daily variation. Both functions are easy to use. The only requirement is that the data are provided in the matrix form. Below we provide the details on the use of these functions.

First, we describe basic requirements for function "SAI". In order to compute a storm index one must input the raw magnetometer records and the coordinates of the stations used. One can use any number of roughly equispaced equatorial stations.The input data should be provided as a matrix. Each column of this data matrix contains the records for each individual station. The coordinates should be written in form of a matrix as well. Each column corresponds to the station, the first row must contain the latitude and the second row -- longitude. This function returns the global storm index estimate.

In order to estimate the daily nonconstant variation, the "SQ" function can be used. First, the storm index must be calculated using the function "SAI". The resulting index is one of the "SQ.new" inputs. We recommend to use the data from at least two stations to estimate the daily variation. The data should be provided in the matrix form. Each column must contain records from different stations. This functions returns Sq estimated for each station individually.