# Publications by Raymond Pierrehumbert

## Decay of passive scalars under the action of single scale smooth velocity fields in bounded two-dimensional domains: from non-self-similar probability distribution functions to self-similar eigenmodes.

Physical review. E, Statistical, nonlinear, and soft matter physics **66** (2002) 056302-

We examine the decay of passive scalars with small, but nonzero, diffusivity in bounded two-dimensional (2D) domains. The velocity fields responsible for advection are smooth (i.e., they have bounded gradients) and of a single large scale. Moreover, the scale of the velocity field is taken to be similar to the size of the entire domain. The importance of the initial scale of variation of the scalar field with respect to that of the velocity field is strongly emphasized. If these scales are comparable and the velocity field is time periodic, we see the formation of a periodic scalar eigenmode. The eigenmode is numerically realized by means of a deterministic 2D map on a lattice. Analytical justification for the eigenmode is available from theorems in the dynamo literature. Weakening the notion of an eigenmode to mean statistical stationarity, we provide numerical evidence that the eigenmode solution also holds for aperiodic flows (represented by random maps). Turning to the evolution of an initially small scale scalar field, we demonstrate the transition from an evolving (i.e., non-self-similar) probability distribution function (pdf) to a stationary (self-similar) pdf as the scale of variation of the scalar field progresses from being small to being comparable to that of the velocity field (and of the domain). Furthermore, the non-self-similar regime itself consists of two stages. Both stages are examined and the coupling between diffusion and the distribution of the finite time Lyapunov exponents is shown to be responsible for the pdf evolution.

## Testing paleogeographic controls on a Neoproterozoic snowball Earth

GEOPHYSICAL RESEARCH LETTERS **29** (2002) ARTN 1515

## The advection-diffusion problem for stratospheric flow. Part II: Probability distribution function of tracer gradients

JOURNAL OF THE ATMOSPHERIC SCIENCES **59** (2002) 2830-2845

## The hydrologic cycle in deep-time climate problems.

Nature **419** (2002) 191-198

Hydrology refers to the whole panoply of effects the water molecule has on climate and on the land surface during its journey there and back again between ocean and atmosphere. On its way, it is cycled through vapour, cloud water, snow, sea ice and glacier ice, as well as acting as a catalyst for silicate-carbonate weathering reactions governing atmospheric carbon dioxide. Because carbon dioxide affects the hydrologic cycle through temperature, climate is a pas des deux between carbon dioxide and water, with important guest appearances by surface ice cover.

## Surface quasigeostrophic turbulence: The study of an active scalar.

Chaos **12** (2002) 439-450

We study the statistical and geometrical properties of the potential temperature (PT) field in the surface quasigeostrophic (SQG) system of equations. In addition to extracting information in a global sense via tools such as the power spectrum, the g-beta spectrum, and the structure functions we explore the local nature of the PT field by means of the wavelet transform method. The primary indication is that an initially smooth PT field becomes rough (within specified scales), though in a qualitatively sparse fashion. Similarly, initially one-dimensional iso-PT contours (i.e., PT level sets) are seen to acquire a fractal nature. Moreover, the dimensions of the iso-PT contours satisfy existing analytical bounds. The expectation that the roughness will manifest itself in the singular nature of the gradient fields is confirmed via the multifractal nature of the dissipation field. Following earlier work on the subject, the singular and oscillatory nature of the gradient field is investigated by examining the scaling of a probability measure and a sign singular measure, respectively. A physically motivated derivation of the relations between the variety of scaling exponents is presented, the aim being to bring out some of the underlying assumptions which seem to have gone unnoticed in previous presentations. Apart from concentrating on specific properties of the SQG system, a broader theme of the paper is a comparison of the diagnostic inertial range properties of the SQG system with both the two- and three-dimensional Euler equations. (c) 2002 American Institute of Physics.

## Abrupt Climate Change: Inevitable Surprises

National Academies Press, 2002

Based on the best and most current research available, this book surveys the history of climate change and makes a series of specific recommendations for the future.

## The advection-diffusion problem for stratospheric flow. Part I: Concentration probability distribution function

JOURNAL OF THE ATMOSPHERIC SCIENCES **58** (2001) 1493-1510

## Impact of ocean dynamics on the simulation of the Neoproterozoic "snowball Earth"

GEOPHYSICAL RESEARCH LETTERS **28** (2001) 1575-1578

## A new approach to stable isotope-based paleoaltimetry: implications for paleoaltimetry and paleohypsometry of the High Himalaya since the Late Miocene

EARTH AND PLANETARY SCIENCE LETTERS **188** (2001) 253-268

## Physical Climate Processes and Feedbacks

in *Climate Change 2001: The Scientific Basis Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change*, Cambridge University Press (2001) 7

Climate Change 2001: The Scientific Basis is the most comprehensive and up-to-date scientific assessment of past, present and future climate change.

## 'Equability' in an unequal world: The early Eocene revisited

GFF **122** (2000) 101-102

## Lattice models of advection-diffusion.

Chaos (Woodbury, N.Y.) **10** (2000) 61-74

We present a synthesis of theoretical results concerning the probability distribution of the concentration of a passive tracer subject to both diffusion and to advection by a spatially smooth time-dependent flow. The freely decaying case is contrasted with the equilibrium case. A computationally efficient model of advection-diffusion on a lattice is introduced, and used to test and probe the limits of the theoretical ideas. It is shown that the probability distribution for the freely decaying case has fat tails, which have slower than exponential decay. The additively forced case has a Gaussian core and exponential tails, in full conformance with prior theoretical expectations. An analysis of the magnitude and implications of temporal fluctuations of the conditional diffusion and dissipation is presented, showing the importance of these fluctuations in governing the shape of the tails. Some results concerning the probability distribution of dissipation, and concerning the spatial scaling properties of concentration fluctuation, are also presented. Though the lattice model is applied only to smooth flow in the present work, it is readily applicable to problems involving rough flow, and to chemically reacting tracers. (c) 2000 American Institute of Physics.

## Spatially correlated and inhomogeneous random advection

PHYSICS OF FLUIDS **12** (2000) 822-834

## Atmospheric pCO(2) sensitivity to the biological pump in the ocean

GLOBAL BIOGEOCHEMICAL CYCLES **14** (2000) 1219-1230

## Climate change and the tropical Pacific: the sleeping dragon wakes.

Proceedings of the National Academy of Sciences of the United States of America **97** (2000) 1355-1358

## Subtropical water vapor as a mediator of rapid global climate change

in *Mechanisms of Global Climate Change at Millennial Time Scales*, American Geophysical Union (1999) 22

Part of a series from Geophysical Monograph Series

## Mixing of an advected-diffused tracer in the lower stratosphere: probability distribution functions of tracer gradients and differences

12TH CONFERENCE ON ATMOSPHERIC AND OCEANIC FLUID DYNAMICS (1999) 303-306

## Spatially inhomogeneous random advection

12TH CONFERENCE ON ATMOSPHERIC AND OCEANIC FLUID DYNAMICS (1999) 307-311

## Huascaran delta O-18 as an indicator of tropical climate during the Last Glacial Maximum

GEOPHYSICAL RESEARCH LETTERS **26** (1999) 1345-1348

## Subtropical water vapor as a mediator of rapid global climate change

in *Geophysical Monograph Series*, **112** (1999) 339-361

© 1999 by the American Geophysical Union. This article surveys the essential features of atmospheric water vapor dynamics needed to address current issues regarding the possible role of water vapor changes in mediating climate fluctuations on the millennial to Milankovic time scales. The focus is on the subtropics, which afford the most interesting possibilities for significant feedbacks. The observed distribution of water vapor, the amount by which water vapor must change in order to cause a significant temperature change, and the physical factors that determine the water vapor content of the subtropical atmosphere are discussed. It is shown that halving the subtropical relative humidity would lead to a 2.5K cooling of the tropics, while doubling it would lead to a 3K warming. The humidity content of the subtropics could be reduced by enhancing subsidence, reducing transient eddy activity, or contracting the convective region. Further work is needed to determine which, if any, of these changes occur in concert with the observed millennial and longer scale climate fluctions.