Resonant Forcing by Solar Declination of Rossby Waves at the Tropopause and Implications in Extreme Events, Precipitation, and Heat Waves—Part 1: Theory

The purpose of this first article is to provide a physical basis for atmospheric Rossby waves at the tropopause to clarify their properties and improve our knowledge of their role in the genesis of extreme precipitation and heat waves. By analogy with the oceanic Rossby waves, the role played by the pycnocline in ocean Rossby waves is replaced here by the interface between the polar jet and the ascending air column at the meeting of the polar and Ferrel cell circulation or between the subtropical jet and the descending air column at the meeting of the Ferrel and Hadley cell circulation. In both cases, the Rossby waves are suitable for being resonantly forced in harmonic modes by tuning their natural period to the forcing period. Here, the forcing period is one year as a result of the variation in insolation due to solar declination. A search for cause-and-effect relationships is performed from the joint representation of the amplitude and phase of (1) the velocity of the cold or warm modulated airflows at 250 mb resulting from Rossby waves, (2) the geopotential height at 500 mb, and (3) the precipitation rate or ground air temperature. This is for the dominant harmonic mode whose period can be 1/16, 1/32, or 1/64 year, which reflects the intra-seasonal variations in the rising and falling air columns at the meeting of the polar, Ferrel, and Hadley cell circulation. Harmonics determine the duration of blocking. Two case studies referring to extreme cold and heat waves are presented. Dual cyclone–anticyclone systems seem to favor extreme events. They are formed by two joint vortices of opposite signs reversing over a period, concomitantly with the involved modulated airflows at the tropopause. A second article will be oriented toward (1) the examination of different case studies in order to ascertain the common characteristics of Rossby wave patterns leading to extreme events and (2) a map of the globe revealing future trends in the occurrence of extreme events.