Disturbances of the geomagnetic field produced by space weather events can have an impact on power systems and other critical infrastructure. To mitigate these risks it is important to determine the extreme values of geomagnetic activity that can occur. More than 40 years of 1 min magnetic data recorded at 13 Canadian geomagnetic observatories have been analyzed to evaluate extreme levels in geomagnetic and geoelectric activities in different locations of Canada. The hourly ranges of geomagnetic field variations and hourly maximum in rate of change of the magnetic variations have been used as measures of geomagnetic activity. Geoelectric activity is estimated by the hourly peak amplitude of the geoelectric fields calculated with the use of Earth resistivity models specified for different locations in Canada. A generalized extreme value distribution was applied to geomagnetic and geoelectric indices to evaluate extreme geomagnetic and geoelectric disturbances, which could happen once per 50 and once per 100 years with 99% confidence interval. Influence of geomagnetic latitude and Earth resistivity models on the results for the extreme geomagnetic and geoelectric activity is discussed. The extreme values provide criteria for assessing the vulnerability of power systems and other technology to geomagnetic activity for design or mitigation purposes.

Analyses of observational data on hurricanes in the tropical atmosphere indicate the existence of spiral rainbands which propagate outward from the eye and affect the structure and intensity of the hurricane. These disturbances may be described as vortex Rossby waves. This paper describes the evolution of barotropic vortex Rossby waves in a cyclonic vortex in a two-dimensional configuration where the variation of the Coriolis force with latitude is ignored. The waves are forced by a constant-amplitude boundary condition at a fixed radius from the center of the vortex and propagate outward. The mean flow angular velocity profile is taken to be a quadratic function of the radial distance from the center of the vortex and there is a critical radius at which it is equal to the phase speed of the waves. For the case of waves with steady amplitude, an exact solution is derived for the steady linearized equations in terms of hypergeometric functions; this solution is valid in the outer region away from the critical radius. For the case of waves with time-dependent amplitude, asymptotic solutions of the linearized equations, valid for late time, are obtained in the outer and inner regions. It is found that there are strong qualitative similarities between the conclusions on the evolution of the vortex waves in this configuration and those obtained in the case of Rossby waves in a rectangular configuration where the latitudinal gradient of the Coriolis parameter is taken into account. In particular, the amplitude of the steady-state outer solution is greatly attenuated and there is a phase change of −π across the critical radius, and in the linear time-dependent configuration, the outer solution approaches a steady state in the limit of infinite time, while the

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Vortex Rossby waves in cyclones in the tropical atmosphere are believed to play a role in the observed eyewall replacement cycle, a phenomenon in which concentric rings of intense rainbands develop outside the wall of the cyclone eye, strengthen and then contract inward to replace the original eyewall. In this paper, we present a two‐dimensional configuration that represents the propagation of forced Rossby waves in a cyclonic vortex and use it to explore mechanisms by which critical layer interactions could contribute to the evolution of the secondary eyewall location. The equations studied include the nonlinear terms that describe wave‐mean‐flow interactions, as well as the terms arising from the latitudinal gradient of the Coriolis parameter. Asymptotic methods based on perturbation theory and weakly nonlinear analysis are used to obtain the solution as an expansion in powers of two small parameters that represent nonlinearity and the Coriolis effects. The asymptotic solutions obtained give us insight into the temporal evolution of the forced waves and their effects on the mean vortex. In particular, there is an inward displacement of the location of the critical radius with time which can be interpreted as part of the secondary eyewall cycle.