While some of my work has involved large scale scientific computation, the hallmark of the work is formulation of idealized conceptual frameworks that lead to models whose behavior can be thoroughly analyzed from a mathematical standpoint. This programme has been carried out over a broad range of problems in fluid dynamics and climate physics, with a general trend over time to incorporation of a richer variety of physical processes.
The nature of the transition from two dimensional to three dimensional turbulence is one of the grand challenges of fluid mechanics. Much conventional fluid stability theory was developed for parallel flow – flows in which streamlines are parallel to each other, as in planar shear flow and circularly symmetric vortices. In my thesis work, I discovered that two-dimensional non-circular coherent vortices, such as form in many planar shear layer or jet flows, succumb to a three-dimensional instability akin to that which dissipates aircraft trailing vortices (Pierrehumbert and Widnall 1982); this instability accounts for many key features of a class of transition to three-dimensionality,. Somewhat later, I found that the instability was universal to a broad class of non-parallel flows (Pierrehumbert 1986) and yields a nonlocal cascade directly to small scales of motion limited only by viscosity. A whole field of literature exploring the ramifications of such instabilities has sprung up. The elliptic instabiity (Pierrehumbert 1986) has also stimulated astrophysical work on closely-related instabilities of tidally distorted accretion disks.
I and my co-workers have made contributions to the understanding of the baroclinic instability that is responsible for much of the north-south heat transport on rotating planets. A pioneering analysis of baroclinic jets with gradual variations in the streamwise direction (Pierrehumbert 1984) cast storm tracks in a new light, which also developed a novel WKB-like technique for constructing eigenmodes of such flows. The technique has found widespread applications in other areas of fluid mechanics. Related work elucidated the linear and nonlinear evolution of spatially localized wave packets on baroclinic jets, deepening the connection with observed baroclinic eddies in the Earth’s atmosphere. An overview of these results, in the context of the general subject of baroclinic instability, is given in Pierrehumbert and Swanson 1995.
In the late 1980’s it became recognized that mixing by incompressible two-dimensional flows has an underlying Hamiltonian structure that allows dynamical systems theory to yield profound insights into the properties of fluid mixing of scalar tracers (e.g. chemical concentrations). In a series of papers beginning with Pierrehumbert 1991 I began to exploit such concepts in the analysis of mixing in planetary atmospheres. This included introduction of the use of finite-time Lyapunov exponents as a mixing diagnostics; in a retrospective on Lagrangian Coherent Structures published in Physics Today, applied mathematician George Haller described this work as ”pioneering.” The advection-diffusion problem also has considerable interest in theoretical physics as a model problem in turbulence theory. Our work has had an important influence on this subject by introducing the concept of ”strange eigenmodes,” the sin-sin area preserving map on the plane, and the computationally efficient lattice map (Pierrehumbert 2000). We have extended the work to the analysis of ”active tracers” such as vorticity, which feed back on the flow creating the mixing. A particularly influential branch of this work was the development of the Surface Quasigeostrophic (SQG) model (introduced in Pierrehumbert Held and Swanson 1994, and followed up in later work published in J. Fluid Mech in collaboration with Isaac Held). SQG theory has important applications to behavior of atmospheres with layers of homogenized potential vorticity (a very common situation), but also has become an important model problem in theoretical fluid dynamics because it is mathematically two-dimensional (and hence amenable to high resolution computation) but shares many of the same cascade features as the less tractable case of 3D turbulence.
Water vapor and cloud feedbacks have a crucial effect on the climates of Earth and other planets. I developed an idealized model of tropical climate based on what later came to be known as the Weak Temperature Gradient (WTG) approximation Pierrehumbert 1995. This model revealed the importances of subsaturated air in subtropical dry zones, which act as ”radiator fins” to cool the climate, and focused attention on the importance of the mechanisms which determine the moisture content of these regions. It also clarified a number of previously confusing aspects of the way cloud feedbacks affect the tropics. A whole school of thinking about tropical climate sprung up around this framework especially after the important later work of Adam Sobel and Christopher Bretherton. The radiatior fin concept has also been invoked in understanding models of the runaway greenhouse threshold that defines the inner edge of the habitable zone for exoplanets.
In a series of papers, my group advanced the understanding of the dynamics governing water vapor subsaturation, which is a key to the strength of water vapor feedback. These papers introduced concepts such as stochastic drying and the advection-condensation model, which drew on his theoretical work on passive tracer mixing. He has also worked on applications of isotopic hydrology to paleoclimate reconstruction, paleo-altimetry and characterization of present-day convection.
On global change issues, my group has contributed extensively to science in the aid of public policy. This includes contributions to reports of the Intergovernmental Panel on Climate Change and the US National Research Council (the operating arm of the National Academy of Sciences), and also a number of essays on energy policy and climate ethics. We have published extensively on serious flaws in current policy related to short-lived climate pollution (e.g. methane) and the effects of agricultural policy on climate. I have been active in science communication, through journalistic essays, and for many years was an active contributor to the RealClimate climate science blog.
Accounting for the at least episodically temperate climate of Early Mars is one of the grand challenges of climate science. In Forget and Pierrehumbert 1997 , the theory of a novel scattering greenhouse effect from CO2 ice clouds was developed, and shown to have the potential to substantially warm Early Mars. Work over the subsequent decades showed that this effect does not provide the whole answer to the climate enigma, but the paper was nonetheless significant in overturning prior notions that formation of CO2 ice clouds would have a catastrophic cooling effect. The paper also awakened attention to the scattering greenhouse effect of a broad class of clouds made of substances that are fairly tranparent to infrared; such effects are now routinely incorporated in planetary climate models.
”Snowball Earth” refers to a state of near-global glaciation, which the Earth appears to have experienced several times in its early history. The work in Pierrehumbert 2014 overturned the notion that the clear-sky greenhouse effect from accumulation of CO2 provided a straightforward route to deglaciation, and identified several previously neglected phenomena that inhibit deglaciation. A subsequent series of papers developed the understanding of the Snowball climate, notably introducing the theory of ”sea glaciers” and the ”mudball” deglaciation mechanism. This work is synthesized and extended in Pierrehumbert et al. 2011. Later work led by my former postdoc, Dorian Abbot, established the role of clouds in deglaciation, a possibility first identified in Pierrehumbert 2002. The Snowball papers lay the groundwork for consideration of Snowball states on exoplanets.
Climate is as much about precipitation as it is about temperature. A synthesis of the many ways that the hydrological cycle affects deep-time paleoclimate was given in Pierrehumbert 2002. A major contribution was the elucidation of the regimes in which atmospheric energetics do or do not constrain the way precipitation scales with temperature. Inasmuch as the precipitation-temperature relation is central to the operation of the silicate-weathering thermostat, these results have significant implications for long term climate evolution on Earth and other planets.
The first radiative-dynamic simulations of Titan’s troposphere and its methane-based hydrological cycle, was carried out in Mitchell and Pierrehumbert 2006. It introduced the insight that despite its low temperature Titan is dynamically similar to a very warm all-Tropics Earth, owing to the thermodynamic parameters of methane vs water condensation.
While my group continues to work on Earth climate problems, relating both to the distant past and the near future, the chief focus of our current work is on exoplanets.
Dim, low-mass M stars are the most common kind of star in the Universe, and their potentially liquid water sustaining habitable zone is so close in that potentially habitable planets are likely to be tide-locked to their stars, presenting always the same face to the star much as the Moon always presents the same face to Earth. A number of advances in the understanding of climates of such planets were introduced in Pierrehumbert 2011. It first highlighted the notion that the nominal habitable zone only confers contingent habitability, and exposed the range of habitable and non-habitable climates a planet in the nominal habitable zone could have. Through carrying out the first three-dimensional simulations of tide-locked planets incorporating a realistic hydrological cycle and surface model, it identified a new habitable state for planets with extensive oceans – the ”eyeball Earth” state. The three dimensional simulations were complemented by a WTG-based theory accounting for the nature of the variations between dayside and nightside surface temperature; such models have now become a common tool in the arsenal of exoplanet climate dynamics. This was also the first paper to remark that silicate weathering could contract the outer edge of the habitable zone – a challenge that has recently blossomed into a significant theme in exoplanet research. The planet candidate which stimulated this paper turned out to be a false positive, but the concepts developed in the paper remain valid and have seen broad application to confirmed exoplanets. The closest exoplanet, Proxima Centauri b, is in a very similar climate regime to that discussed in Pierrehumbert 2011. Follow-on papers have continued to develop the understanding of the general circulation of tide-locked terrestrial planets, in particular resolving several outstanding issues about the way the simulated circulation relates to equatorial wave concepts developed to understand the Earth’s tropical circulation.
Outside of astrophysics, it was little appreciated that in sufficient quantities H2 can be a potent greenhouse gas In Pierrehumbert and Gaidos 2011 it was shown that this effect can extend the outer edge of the liquid-water habitable zone to exoplanets far beyond the conventional value defined by CO2. This has sparked intensified interest in the possibility of rocky planets with hydrogen-rich atmospheres. In Wordsworth and Pierrehumbert 2013 it was shown that the N2 - H2 collisional greenhouse effect can lead to substantial warming that could be of importance to the Faint Young Sun period of Early Earth. A closely related effect was later shown by others to significantly warm Early Mars, and both collisional greenhouse affects expand our picture of the kind of atmosphere that can make a planet habitable.
The importance of background atmospheric gases such as N2 was identified in Wordsworth and Pierrehumbert 2014, which presented a realizable scenario leading to massive abiotic accumulation of O2. This has become a standard reference in the biosignature literature, and was one of the key papers that led to the present understanding that O2 alone is not a biosignature.
The diversity of exoplanets has required a virtual reinvention of climate dynamics, in order to meet the challenge of understanding the new diversity of climate regimes. In Earth’s present climate, the main condensible substance (water vapor) is a minor constituent of the atmosphere, but situations in which the condensible (which need not be water) is a major constituent are expected to be common in exoclimates. The foundations of a general theory of such atmospheres were laid out in Pierrehumbert and Ding 2016. ”Lava planets” are another novel climate regime; these planets are in such close orbit to their stars that they have a permanent dayside magma ocean. They were expected to have thin mineral-vapor atmospheres, but observations of the planet 55 Cancri-e can only be explained if there is substantial heat transport to the nightside. In Hammond and Pierrehumbert 2017 the first three dimensional simulations of a lava planet were presented, and the results showed that a thick noncondensible atmosphere could explain most features of the observations, and characterized what kinds of atmospheres were most consistent with observation.
My approach to climate physics is codified in my textbook Principles of Planetary Climate, which has become a standard route by which new researchers enter the field of exoplanet climate. In a review of the book in Physics Today, noted planetary scientist Peter Gierasch described it as ”a triumph.” The book contains many original research results, such as the insight that the outer limits of the habitable zone are constrained by a generalized form of the runaway greenhouse, and the dependence of the runaway greenhouse threshold on surface gravity. It has unified the approach to deep-time Earth paleoclimate, climate of Solar System planets and to exoclimate. It has introduced the exoplanet community to important mechanisms such as silicate weathering formerly only appreciated in the Earth Systems community. Many of the problems set in the book have led to publications (for example Wordsworth and Pierrehumbert 2014, which originated in the ”Springtime for Europa” problem). My group was among the first to adopt Python as a language for climate modeling, and the software accompanying the book for many was the entry point to scientific programming in Python; it also provided a madeling framework on which original research could be based (e.g. the H2 greenhouse calculations in Pierrehumbert and Gaidos 2011).