# Publications

## Historical Overview of Climate Change Science

in *Intergovernmental Panel on Climate Change (IPCC), 4th Assessment Report, Working Group 1: The Physical Basis of Climate Change*, (2007) 1

## How good is an ensemble an capturing truth? Using bounding boxes for forecast evaluation

Quarterly Journal of the Royal Meteorological Society **133** (2007) 1309-1325

Ensemble prediction systems aim to account for uncertainties of initial conditions and model error. Ensemble forecasting is sometimes viewed as a method of obtaining (objective) probabilistic forecasts. How is one to judge the quality of an ensemble at forecasting a system? The probability that the bounding box of an ensemble captures some target (such as 'truth' in a perfect model scenario) provides new statistics for quantifying the quality of an ensemble prediction system: information that can provide insight all the way from ensemble system design to user decision support. These simple measures clarify basic questions, such as the minimum size of an ensemble. To illustrate their utility, bounding boxes are used in the imperfect model context to quantify the differences between ensemble forecasting with a stochastic model ensemble prediction system and a deterministic model prediction system. Examining forecasts via their bounding box statistics provides an illustration of how adding stochastic terms to an imperfect model may improve forecasts even when the underlying system is deterministic. Copyright © 2007 Royal Meteorological Society.

## Using numerical weather prediction to assess climate models

QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY **133** (2007) 129-146

## Another look at stochastic condensation for subgrid cloud modeling: Adiabatic evolution and effects

Journal of the Atmospheric Sciences **64** (2007) 3949-3969

The theory of stochastic condensation, which models the impact of an ensemble of unresolved supersaturation fluctuations S′ on the volume-averaged droplet-size distribution f (r), is revisited in the modern context of subgrid cloud parameterization. The exact transition probability density for droplet radius driven by independent, Gaussian S′ fluctuations that are periodically renewed is derived and shown to be continuous but not smooth. The Fokker-Planck model follows naturally as the smooth-in-time approximation to this discrete-in-time process. Evolution equations for the moments of f(r) that include a contribution from subgrid S′ fluctuations are presented; these new terms are easily implemented in moment-based cloud schemes that resolve supersaturation. New, self-consistent expressions for the evolution of f(r) and mean supersaturation S̄ in a closed, adiabatic volume are derived without approximation; quite appropriately, these coupled equations exactly conserve total water mass. The behavior of this adiabatic system, which serves as a surrogate for a closed model grid column, is analyzed in detail. In particular, a new nondimensional number is derived that determines the relative impact of S′ fluctuations on droplet spectral evolution, and the contribution of fluctuations to S̄ is shown to be negative definite and maximal near the accommodation length and has a direct correspondence to the analysis of Cooper. Observational support for the theory of stochastic condensation is found in cloud droplet spectra from cumulus cloud fields measured during the Rain in the Cumulus over the Ocean (RICO) and Small Cumulus Microphysics Study (SCMS) campaigns. Increasing spectral broadening with increasing spatial scale is discovered and compares well with theoretical predictions. However, the observed spectra show evidence of non-Gaussian S′ fluctuations and inhomogeneous mixing, processes neglected in the current theory.

## Ensemble decadal predictions from analysed initial conditions.

Philos Trans A Math Phys Eng Sci **365** (2007) 2179-2191

Sensitivity experiments using a coupled model initialized from analysed atmospheric and oceanic observations are used to investigate the potential for interannual-to-decadal predictability. The potential for extending seasonal predictions to longer time scales is explored using the same coupled model configuration and initialization procedure as used for seasonal prediction. It is found that, despite model drift, climatic signals on interannual-to-decadal time scales appear to be detectable. Two climatic states have been chosen: one starting in 1965, i.e. ahead of a period of global cooling, and the other in 1994, ahead of a period of global warming. The impact of initial conditions and of the different levels of greenhouse gases are isolated in order to gain insights into the source of predictability.

## Another look at stochastic condensation in clouds: Exact solutions, fokker-planck approximations and adiabatic evolution

12th Conference on Cloud Physics, and 12th Conference on Atmospheric Radiation (2006)

In this manuscript - which closely follows Jeffery et al. (2006) - we have taken "another look" at stochastic condensation in the hope of clarifying the earlier derivations and fully exploring the implications of this theory. In contrast to the derivations of Levin and Sedunov (1966a, b) and Manton (1979), we begin with a simple model of stochastic condensation - independent, Gaussian supersaturation fluctuations (S′) renewed after a time τ - that is exactly solvable. This model is trivial to simulate on a computer and can be used to compare and contrast Lagrangian and Eulerian approaches for modeling droplet spectra (Andrejczuk et al. 2006). The Fokker-Planck approximation to this exact solution follows by replacing the discrete sampling of S′ with its continuous surrogate. The Fokker-Planck diffusivity and operator are thus seen to be the natural smooth-in-time approximation to a discrete-in-time process. We have also taken another - look at the equation for the mean supersaturation, S̄, in the presence of S′ fluctuations modeled using the Levin-Sedunov-Mazin Fokker-Planck operator. While this problem is treated in an approximate fashion (and with little transparency) in Voloshchukand Sedunov (1977), we derive the expression for (S′|r) without approximation and show how this expression "closes" the S̄-equation self-consistently, thereby ensuring that total water mass is exactly conserved. Using the quasi-stationary (QS) evaluation of S̄, we derive the exact correction term to S (i.e. the S′ contribution corresponding to the Levin-Sedunov-Mazin model). The correction term is negative definite, peaks in magnitude when (r) is near the accommodation length (≈ 2 μm), and decays as (r) as the droplet spectrum grows to large sizes. This exact result has a direct correspondence to the analysis of Cooper (1989). Using our self-consistent equation for S̄, we evaluate spectral broadening in an adiabatic parcel and find some broadening to larger sizes (consistent with earlier estimates, e.g. Manton (1979)), but a more significant decrease in 〈r〉 at fixed liquid water content which may have implications for modeled cloud reflectivity. While the proceeding discussion is largely a clarification and elucidation of previous work, most notably Voloshchuk and Sedunov (1977), we have also extended the theory of stochastic condensation by deriving the non-dimensional number, N, that determines the relative impact of S′-fluctuations on droplet spectral evolution in an adiabatic volume and in the QS limit. For constant updraft velocity and Fokker-Planck diffusivity, N is also a constant, ranging from 10 to 10 for typical atmospheric conditions and model grid sizes when the assumed S′-standard deviation is 1%. We find significant spectral broadening, and in particular decreasing 〈r〉, for N > 1, and discover that S̄ can be negative in a rising adiabatic parcel when ND > 6.5 for droplets of zero initial size. Using in-situ droplet spectra from cumulus cloud fields observed during the RICO and SCMS field campaigns, we have verified a seminal prediction of the theory of stochastic condensation - increasing broadening with increasing spatial scale - by averaging the observed spectra over segments containing one or more clouds. In addition, scale-dependent values of N retrieved from the segment-averaged spectra using our adiabatic model show good consistency with the previously discussed theoretical estimates. We believe this encouraging result to be the first observational confirmation of the stochastic condensation mechanism and the decades-old, pioneering work of Levin-Sedunov-Mazin. Moreover, these results suggest that the parameterization of unresolved S′-fluctuations using Fokker-Planck theory or other means will become increasingly important as explicit (bin) microphysics schemes are applied at larger scales (Lynn et al. 2005), where an increasing fraction of individual clouds are, themselves, unresolved. However, important differences between the observed and modeled droplet spectra are also observed. In particular, the observed spectra suggest non-Gaussian S′ fluctuations and the inhomogeneous mixing process of Baker et al. (1980). Further work is needed to assess the impact of non-Gaussian S′-fluctuations and large renewal times on droplet spectral broadening and to derive differential operators that can model their ensemble effect in the equations of cloud physics.

## Cloud-clear air interfacial mixing: Anisotropy of turbulence generated by evaporation of liquid water. Laboratory observations and numerical modelling

12th Conference on Cloud Physics, and 12th Conference on Atmospheric Radiation (2006)

Small scale mixing of cloud with unsaturated environment is investigated in numerical simulations (spatial resolution of 2.5mm) and in laboratory cloud chamber experiments by means of Particle Image Velocimetry (PIV) with spatial resolution of 0.07mm. Despite substantial differences in physical conditions and various spatial resolutions (resolving well the dissipation scale in the laboratory and applying grid length larger than the Kolmogorov scale in the simulation), results of both investigations indicate that small-scale turbulence in such conditions is highly anisotropic with the preferred direction in the vertical. Buoyancy forces resulting from evaporation of cloud droplets substantially influence smallest scales of turbulence. The vertical direction, in which buoyancy force acts, is preferred. Typically, <(u′) > is about two times smaller than <(w′)>. The probability distribution functions of w′ are wider than those of u′. It is still uncertain to what extent these results apply to real clouds. In situ measurements of turbulent velocity fluctuations from various types of clouds are necessary to validate common assumptions of small-scale cloud isotropy.

## Malaria early warnings based on seasonal climate forecasts from multi-model ensembles

NATURE **439** (2006) 576-579

## Impact of increasing greenhouse gas concentrations in seasonal ensemble forecasts

GEOPHYSICAL RESEARCH LETTERS **33** (2006) ARTN L07708

## Changing frequency of occurrence of extreme seasonal temperatures under global warming (vol 32, art no L20721, 2005)

GEOPHYSICAL RESEARCH LETTERS **33** (2006) ARTN L07712

## Numerical simulation of cloud-clear air interfacial mixing: Effects on cloud microphysics

Journal of the Atmospheric Sciences **63** (2006) 3204-3225

This paper extends the previously published numerical study of Andrejczuk et al. on microscale cloud-clear air mixing. Herein, the primary interest is on microphysical transformations. First, a convergence study is performed - with well-resolved direct numerical simulation of the interfacial mixing in the limit - to optimize the design of a large series of simulations with varying physical parameters. The principal result is that all conclusions drawn from earlier low-resolution (Δx = 10 m) simulations are corroborated by the high-resolution (Δx = 0.25 × 10 m) calculations, including the development of turbulent kinetic energy (TKE) and the evolution of microphysical properties. This justifies the use of low resolution in a large set of sensitivity simulations, where microphysical transformations are investigated in response to variations of the initial volume fraction of cloudy air, TKE input, liquid water mixing ratio in cloudy filaments, relative humidity (RH) of clear air, and size of cloud droplets. The simulations demonstrate that regardless of the initial conditions the evolutions of the number of cloud droplets and the mean volume radius follow a universal path dictated by the TKE input, RH of clear air filaments, and the mean size of cloud droplets. The resulting evolution path only weakly depends on the progress of the homogenization. This is an important conclusion because it implies that a relatively simple rule can be developed for representing the droplet-spectrum evolution in cloud models that apply parameterized microphysics. For the low-TKE input, when most of the TKE is generated by droplet evaporation during mixing and homogenization, an inhomogencous scenario is observed with approximately equal changes in the dimensionless droplet number and mean volume radius cubed. Consistent with elementary scale analysis, higher-TKE inputs, higher RH of cloud-free filaments, and larger cloud droplets enhance the homogeneity of mixing. These results are discussed in the context of observations of entrainment and mixing in natural clouds. © 2006 American Meteorological Society.

## Erratum: "Changing frequency of occurrence of extreme seasonal temperatures under global warming" (Geophysical Research Letters (2005) vol. 32 10.1029/2005GL023365)

Geophysical Research Letters **33** (2006)

## Developments in dynamical seasonal forecasting relevant to agricultural management

CLIMATE RESEARCH **33** (2006) 19-26

## Changing frequency of occurrence of extreme seasonal temperatures under global warming

Geophysical Research Letters **32** (2005) 1-5

Using a multi-model multi-scenario ensemble of integrations made for the forthcoming fourth assessment report of the Intergovernmental Panel on Climate Change, the frequency of occurrence of extreme seasonal temperatures at the end of the 21st Century is estimated. In this study an extreme temperature is defined as lying above the 95 percentile of the simulated temperature distribution for 20th Century climate. The model probability of extreme warm seasons is heterogeneous over the globe and rises to over 90% in large parts of the tropics. This would correspond to an average return period of such anomalous warm seasons of almost one year. The reliability of these results is assessed using the bounding box technique, previously used to quantify the reliability of seasonal climate forecasts. It is shown that the dramatic increase in extreme warm seasons arises from the combined effect of a shift and a broadening of the temperature distributions. Copyright 2005 by the American Geophysical Union.

## Quantum reality complex numbers, and the meteorological butterfly effect

BULLETIN OF THE AMERICAN METEOROLOGICAL SOCIETY **86** (2005) 519-+

## The rationale behind the success of multi-model ensembles in seasonal forecasting - I. Basic concept

TELLUS SERIES A-DYNAMIC METEOROLOGY AND OCEANOGRAPHY **57** (2005) 219-233

## Representing model uncertainty in weather and climate prediction

ANNUAL REVIEW OF EARTH AND PLANETARY SCIENCES **33** (2005) 163-193

## Probabilistic prediction of climate using multi-model ensembles: from basics to applications.

Philos Trans R Soc Lond B Biol Sci **360** (2005) 1991-1998

The development of multi-model ensembles for reliable predictions of inter-annual climate fluctuations and climate change, and their application to health, agronomy and water management, are discussed.