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Ewan Short
Todd P. Lane
Craig H. Bishop
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Matthew C. Wheeler


Diurnal processes play a primary role in tropical weather. A leading hypothesis is that atmospheric gravity waves diurnally forced near coastlines propagate both offshore and inland, encouraging convection as they do so. In this study we extend the linear analytic theory of diurnally forced gravity waves, allowing for discontinuities in stability and for linear changes in stability over a finite-depth “transition layer.” As an illustrative example, we first consider the response to a commonly studied heating function emulating diurnally oscillating coastal temperature gradients, with a low-level stability change between the boundary layer and troposphere. Gravity wave rays resembling the upper branches of “Saint Andrew’s cross” are forced along the coastline at the surface, with the stability changes inducing reflection, refraction, and ducting of the individual waves comprising the rays, with analogous behavior evident in the rays themselves. Refraction occurs smoothly in the transition-layer solution, with substantially less reflection than in the discontinuous solution. Second, we consider a new heating function which emulates an upper-level convective heating diurnal cycle, and consider stability changes associated with the tropical tropopause. Reflection, refraction, and ducting again occur, with the lower branches of Saint Andrew’s cross now evident. We compare these solutions to observations taken during the Years of the Maritime Continent field campaign, noting better qualitative agreement with the transition-layer solution than the discontinuous solution, suggesting the tropopause is an even weaker gravity wave reflector than previously thought.

Significance Statement

This study extends our theoretical understanding of how forced atmospheric gravity waves change with atmospheric structure. Gravity wave behavior depends on atmospheric stability: how much the atmosphere resists vertical displacements of air. Where stability changes, waves reflect and refract, analogously to when light passes from water to air. Our study presents new mathematical tools for understanding this reflection and refraction, demonstrating reflection is substantially weaker when stability increases over “transition layers,” than when stability increases suddenly. Our results suggest the tropical tropopause reflects less gravity wave energy than previously thought, with potential design implications for weather and climate models, to be assessed in future work.

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