DISSERTATION THE DYNAMICS OF HADLEY CIRCULATION VARIABILITY AND CHANGE Submitted by Nicholas Alexander Davis Department of Atmospheric Science In partial fulfillment of the requirements For the Degree of Doctor of Philosophy Colorado State University Fort Collins, Colorado Summer 2017 Doctoral Committee: Advisor: Thomas Birner David A. Randall Elizabeth A. Barnes Subhas K. Venayagamoorthy William J. Randel Copyright by Nicholas Alexander Davis 2017 All Rights Reserved ABSTRACT THE DYNAMICS OF HADLEY CIRCULATION VARIABILITY AND CHANGE The Hadley circulation exerts a dominant control on the surface climate of earth's tropical belt. Its converging surface winds fuel the tropical rains, while subsidence in the subtropics dries and stabilizes the atmosphere, creating deserts on land and stratocumulus decks over the oceans. Because of the strong meridional gradients in temperature and precipitation in the subtropics, any shift in the Hadley circulation edge could project as major changes in surface climate. While climate model simulations predict an expansion of the Hadley cells in response to greenhouse gas forcings, the mechanisms remain elusive. An analysis of the climatology, variability, and response of the Hadley circulation to radiative forcings in climate models and reanalyses illuminates the broader landscape in which Hadley cell expansion is realized. The expansion is a fundamental response of the atmosphere to increasing greenhouse gas concentrations as it scales with other key climate system changes, including polar amplification, increasing static stability, stratospheric cooling, and increasing global-mean surface temperatures. Multiple measures of the Hadley circulation edge latitudes co-vary with the latitudes of the eddy-driven jets on all timescales, and both exhibit a robust poleward shift in response to forcings. Further, across models there is a robust coupling between the eddy-driving on the Hadley cells and their width. On the other hand, the subtropical jet and tropopause break latitudes, two common observational proxies for the tropical belt edges, lack a strong statistical relationship with ii the Hadley cell edges and have no coherent response to forcings. This undermines theories for the Hadley cell width predicated on angular momentum conservation and calls for a new framework for understanding Hadley cell expansion. A numerical framework is developed within an idealized general circulation model to isolate the mean flow and eddy responses of the global atmosphere to radiative forcings. It is found that it is primarily the eddy response to greenhouse-gas-like forcings that causes Hadley cell expansion. However, the mean flow changes in the Hadley circulation itself crucially mediate this eddy response such that the full response comes about due to eddy-mean flow interactions. A theoretical scaling for the Hadley cell width based on moist static energy is developed to provide an improved framework to understand climate change responses of the general circulation.The scalingpredicts that expansion is driven by increases in the surface latent heat flux and the width of the rising branch of the circulation and opposed by increases in tropospheric radiative cooling. A reduction in subtropical moist static energy flux divergence by the eddies is key, as it tilts the energetic balance in favor of expansion. iii ACKNOWLEDGEMENTS I thank my committee for their invaluable comments and guidance on this dissertation, and my family and friends for their support and understanding. Thomas, you have helped me hone a skeptical eye toward my own research, taught me patience, and instilled in me the willingness to take the hard path. You can never get lost on an adventure. iv TABLE OF CONTENTS ABSTRACT . ii ACKNOWLEDGEMENTS . iv 1 The Hadley Circulation . 1 1.1 The Hadley Cells and the Tropical Belt . 5 1.2 Modeling . 8 1.3 Potential mechanisms for change . 11 2 The Hadley Circulation Response to Greenhouse Gas Forcings . 15 2.1 Climatology . 18 2.2 Temperature response . 20 2.3 Tropical belt width response . 22 2.4 Inter-model differences in the tropical width response and associated thermo- dynamic changes . 29 2.5 Summary . 34 3 The Hadley Circulation in Realistic Forcing Scenarios . 39 3.1 Data . 42 3.2 Tropical belt metrics . 44 3.2.1 Hadley cell edge latitudes, R Ψdp .................... 44 3.2.2 Subtropical jet latitudes, Umax ...................... 46 3.2.3 Tropopause break latitudes, ∆θ ..................... 47 R 3.2.4 Latitudes of maximum downwelling, @y Ψdp . 48 3.2.5 Latitudes of zero surface zonal wind, Usfc . 48 3.2.6 Latitudes of the 500 hPa Hadley cell edge, Ψ500 . 49 3.2.7 Eddy-driven jet metric . 50 3.2.8 Surface climate indices: min(P-E), P-E=0, and area of P-E<0 . 50 3.3 Calculation details . 51 3.3.1 Reanalysis-mean time series . 52 3.4 Temporal and inter-model co-variability . 52 3.4.1 Historical trends in the tropical belt width . 59 3.4.2 Projected trends in the tropical belt width . 65 3.4.3 Relation to the eddy-driven jet . 68 3.4.4 Connection to surface climate . 71 3.5 Summary of trend, variability results . 73 3.6 Relationship to Rossby wave fluxes . 80 3.6.1 Tropical belt grid size effect . 82 3.6.2 Eddy-grid size effect . 85 3.6.3 Estimating eddy fluxes from time-mean fields . 87 3.6.4 Eddy momentum flux-grid size effect . 91 v 3.6.5 Impact of the effect on the Hadley cell width . 93 3.6.6 Summary of the grid size effect . 98 4 Physical Processes Governing the Expansion of the Hadley Circulation . 103 4.1 Response to Greenhouse Gas-like Forcings . 105 4.2 Axisymmetric vs. wave-permitting model . 110 4.3 General characteristics of expansion . 119 4.4 An energy flux perspective . 127 5 A theory for the width of the Hadley circulation . 142 5.1 Eddy effects . 153 5.2 The moisture-driven response . 155 5.3 Assessing the mechanism for expansion . 161 5.4 Comparison to the Held-Hou theory . 164 6 Conclusions . 168 References . 174 Appendix: Governing Physics and Description of the Idealized Gray Radiation Aqua- planet Model (GRAM) . 186 1 Newton's First Law and the Material Derivative on a Rotating Earth . 186 2 Governing Equations . 188 3 Surface Properties . 193 4 Surface Fluxes . 193 5 Diffusivity . 196 6 Moisture . 197 7 Convective Adjustment . 198 8 Radiation . 202 8.1 Optical Depth . 202 8.2 Radiative Heating and Cooling . 207 9 Dynamical Core . 209 9.1 Vertical Differencing . 210 9.2 Discretization . 212 9.3 Spectral Formulation . 215 9.4 Integration Scheme . 217 vi 1 The Hadley Circulation It was inevitable that the Hadley circulation would become a major focus of early atmospheric science. Three hundred years ago, the idea of unraveling the physics governing passing weather disturbances in the midlatitudes and the afternoon thunderstorms in the tropics must have seemed impossible. By contrast the steady surface easterlies and westerlies, each occupying distinct zones on the earth, must have seemed like a good place to start. It's tempting to argue that our understanding of the Hadley circulation has progressed substantially beyond the ideas of its namesake, George Hadley, in 1735. But perhaps it's worth examining Hadley's own words to decide how much they've been rewritten rather than merely refined. In 1686, Edmund Halley crafted a model of the general circulation from hand-drawn maps of surface winds over the oceans. Previous scholars had thought that the rotation of the earth on its axis produced the tropical easterlies, or \ trade winds", as the \loose air" let the rotating surface of the earth rotate past. Halley challenged this notion and instead argued that the sun drove the winds. He imagined that as the sun passed over the earth, it heated the air directly below, and as the sun moved from east to west, the cooler air far to the east would rush in toward the west and toward the equator to try to fill in the less-dense air heated by the sun. Through mass continuity, Halley thought air must be constantly rising on the equator and flowing poleward. While his proposed mechanism for the trade winds was wrong, it had at least introduced the sun as a thermodynamic driver of the circulation. 1 It was George Hadley, a lawyer and amateur meteorologist, who captured the essence of the circulation that now bears his name. Hadley's model was a pioneering combination of ideas that are still as worth pondering today as they were in 1735 (Hadley, 1735): Thus I think the N.E. Winds on this Side of the Equator, and the S.E. on the other Side, are fully accounted for. The same Principle as necessarily extends to the Production of the West Trade-Winds without the Tropicks; the Air rarefied by the Heat of the Sun about the Equatorial Parts, being removed to make room for the Air from the cooler Parts, must rise upwards from the Earth, and as it is a Fluid, will then spread itself abroad over the other Air, and so its Motion in the upper Regions must be to the N. and S. from the Equator. Being got up at a Distance from the Surface of the Earth, it will soon lose great Part of its Heat, and thereby acquire Density and Gravity sufficient to make it approach its Surface again, which may be supposed to be by that Time 'tis arrived at those Parts beyond the Tropicks where the Westerly Winds are found. Being suppos'd at first to have the Velocity of the Surface of the Earth at the Equator, it will have a greater Velocity than the Parts it now arrives at; and thereby become a westerly Wind, with Strength proportionable to the Difference of Velocity, which in several Revolutions will be reduced to a certain Degree, as is laid before, of the Easterly Winds, at the Equator.