# Publications

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

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

## 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, S̄FP, 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)FP without approximation and show how this expression "closes" the S̄FP-equation self-consistently, thereby ensuring that total water mass is exactly conserved. Using the quasi-stationary (QS) evaluation of S̄FP, we derive the exact correction term to SFP, QS (i.e. the S′ contribution corresponding to the Levin-Sedunov-Mazin model). The correction term is negative definite, peaks in magnitude when (r)r is near the accommodation length (≈ 2 μm), and decays as (r-1)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 S̄FP, 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 〈r2〉 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, ND, 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, ND is also a constant, ranging from 10-2 to 102 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 〈r2〉r, for ND > 1, and discover that S̄FP, QS 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 ND 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′) 2> is about two times smaller than <(w′)2>. 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.

## Influence of a stochastic parameterization on the frequency of occurrence of North Pacific weather regimes in the ECMWF model

GEOPHYSICAL RESEARCH LETTERS **32** (2005) ARTN L23811

## 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

## Recurrent climate winter regimes in reconstructed and modelled 500 hPa geopotential height fields over the North Atlantic/European sector 1659-1990

CLIMATE DYNAMICS **24** (2005) 809-822

## A new view of seasonal forecast skill: Bounding boxes from the DEMETER ensemble forecasts

Tellus, Series A: Dynamic Meteorology and Oceanography **57** (2005) 265-279

Insight into the likely weather several months in advance would be of great economic and societal value. The DEMETER project has made coordinated multi-model, multi-initial-condition simulations of the global weather as observed over the last 40 years; transforming these model simulations into forecasts is non-trivial. One approach is to extract merely a single forecast (e.g. best-first-guess) designed to minimize some measure of forecast error. A second approach would be to construct a full probability forecast. This paper explores a third option, namely to see how often this collection of simulations can be said to capture the target value, in the sense that the target lies within the bounding box of the forecasts. The DEMETER forecast system is shown to often capture the 2-m temperature target in this sense over continental areas at lead times up to six months. The target is captured over 95% of the time at over a third of the grid points and maintains a bounding box range less than that of the local climatology. Such information is of immediate value from a user's perspective. Implications for the minimum ensemble size as well as open foundational issues in translating a set of multi-model multi-initial-condition simulations into a forecast are discussed; in particular, those involving 'bias correction' are consider. Copyright © Blackwell Munksgaard, 2005.

## A forecast quality assessment of an end-to-end probabilistic multi-model seasonal forecast system using a malaria model

TELLUS SERIES A-DYNAMIC METEOROLOGY AND OCEANOGRAPHY **57** (2005) 464-475

## 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 - II. Calibration and combination

TELLUS SERIES A-DYNAMIC METEOROLOGY AND OCEANOGRAPHY **57** (2005) 234-252

## 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.

## Representing model uncertainty in weather and climate prediction

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

## Improved radio occultation sounding of the Arctic atmosphere using simulations with a high resolution atmospheric model

Physics and Chemistry of the Earth **29** (2004) 277-286

Radio occultation experiments have been simulated for the Arctic region on the basis of the regional atmospheric model HIRHAM4. Irregular structures in the atmosphere produce a violation of the quasi-sphericity in the radio signal propagation and exert a strong influence on the accuracy of atmospheric profiles retrieved by the radio occultation technique. Errors in radio occultation data are spatially localised and associated with gradients in atmospheric structures. Local errors reach 2% in retrieved profiles of refractivity corresponding to an error of 6 K in temperature. Therefore mesoscale variations in atmospheric parameter gradients in a specified region must be taken into account when interpreting radio occultation data. We show, that a correction functional can be developed using the refractivity index field calculated from the regional model in order to improve the radio occultation retrieval of atmospheric parameters. This functional is constructed from instantaneous model outputs, as well as from temporally averaged fields of refractivity using data of the HIRHAM4 model for the Arctic atmosphere. The correction functional derived from monthly averaged data reduced the retrieval errors of refractivity, temperature, and pressure in the troposphere, in particular, temperature retrieval errors are reduced up to 1 K. Application of this kind of functional depends on whether the model used for the construction of the functional is able to simulate the real mesoscale atmospheric structures. © 2004 Elsevier Ltd. All rights reserved.

## Internal climate variability in global and regional climate models

CLIMATE IN HISTORICAL TIMES: TOWARDS A SYNTHESIS OF HOLOCENCE PROXY DATA AND CLIMATE MODELS (2004) 365-382

## Gradient free descent: Shadowing, and state estimation using limited derivative information

Physica D: Nonlinear Phenomena **190** (2004) 153-166

Shadowing trajectories can play an important role in assessing the reliability of forecasting models, they can also play an important role in providing state estimates for ensemble forecasts. Gradient descent methods provide one approach for obtaining shadowing trajectories, which have been shown to have many useful properties. There remains the important question whether shadowing trajectories can be found in very high-dimensional systems, like weather and climate models. The principle impediment is the need to compute the derivative (or adjoint) of the system dynamics. In this paper we investigate gradient descent methods that use limited derivative information. We demonstrate the methods with an application to a moderately high-dimensional system using no derivative information at all. © 2003 Elsevier B.V. All rights rserved.

## Numerical simulation of cloud- clear air interfacial mixing

Journal of the Atmospheric Sciences **61** (2004) 1726-1739

This paper discusses results from a series of direct numerical simulations of the microscale cloud-clear air mixing, set forth in the idealized scenario of decaying moist turbulence. In the moist case, kinetic energy of microscale motions comes not only from the classical downscale energy cascade, but it can also be generated internally due to the evaporation of cloud droplets. Three sets of numerical simulations are performed for three intensities of initial large-scale eddies. In each set, a control dry simulation is performed, as well as two moist simulations applying either bulk or detailed representation of cloud microphysics. Model results suggest that, as far as the evolutions of enstrophy and turbulent kinetic energy are concerned, the most significant impact of moist processes occurs at the low intensity of initial large-scale eddies (the input turbulent kinetic energy of 2 X 10 m s resulting in the maximum eddy dissipation rate of 5 X 10 m s). In such a case, mixing and homogenization are dominated by the kinetic energy generated as a result of evaporation of cloud water and its impact on the microscale buoyancy. Detailed microphysics, which explicitly treat the size dependence of cloud droplet sedimentation and evaporation, appear to have a comparatively small effect, although this result might be an artifact of a coarse grid resolution used in the simulations. High anisotropy, also observed in laboratory experiments with mixing, between cloudy and cloud-free air, prevails even at the high intensity of initial large-scale eddies (the input turbulent kinetic energy of 2 X 10 m s, the maximum eddy dissipation rate of 7 × 10 m s), despite the fact that mixing and homogenization proceed in a similar manner in moist and dry simulations. Impact on cloud microphysics is also quantified. Cloud droplet spectra at the end of simulations correspond to neither the extremely inhomogeneous nor homogeneous mixing scenarios-the two asymptotic limits where, respectively, either the cloud droplet size or the number of cloud droplets remain constant. The shift from low to high intensity of initial large-scale eddies shifts the mixing scenario toward the homogeneous case, corroborating the classical argument based on scale analysis. © 2004 American Meteorological Society.

## Nonlinear dynamics of the climate system

CLIMATE IN HISTORICAL TIMES: TOWARDS A SYNTHESIS OF HOLOCENCE PROXY DATA AND CLIMATE MODELS (2004) 13-41

## A granular permutation-based representation of complex numbers and quaternions: elements of a possible realistic quantum theory

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES **460** (2004) 1039-1055