HMMHSMM (version 0.1.0)

weekly_maxima: Weekly maxima of geomagnetic rate-of-change data from Eskdalemuir Magnetic Observatory

Description

A dataset containing weekly block maxima of the horizontal geomagnetic field rate-of-change at the Eskdalemuir Magnetic Observatory, Scotland, United Kingdom. These data quantify the variability of the Earth's magnetic field and capture periods of extreme geomagnetic disturbance from 1999 to 2022.

Usage

data(weekly_maxima)

Format

A numeric vector of weekly maxima of $$R_1(t) = \sqrt{(X_t - X_{t-1})^2 + (Y_t - Y_{t-1})^2},$$ where \(X_t\) and \(Y_t\) are the horizontal north and east components of the Earth's magnetic field, respectively, measured at one-minute intervals.

Details

Aggregating to a weekly scale smooths out short-lived fluctuations while retaining the most significant geomagnetic disturbances, as well as reducing short-term serial dependencies. The extreme nature of the data motivates modelling via the Generalised Extreme Value (GEV) distribution, with density $$f(x) = \frac{1}{\sigma} \left[1+\xi\left(\frac{x-\mu}{\sigma}\right)\right]^{-\frac{1}{\xi}-1} \exp\left\{-\left[1+\xi\left(\frac{x-\mu}{\sigma}\right)\right]^{-\frac{1}{\xi}}\right\},$$ where \(\mu\), \(\sigma\), and \(\xi\) are the location, scale, and shape parameters, respectively.

Examples

data(weekly_maxima)
hist(weekly_maxima, breaks = 30, main = "Weekly maxima of geomagnetic variability",
     xlab = "Weekly maximum rate of change (nT/min)")