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Erich Becker and Ulrike Burkhardt

1. Introduction Atmospheric circulation models that resolve synoptic-scale waves need to contain horizontal diffusion in order to prevent the accumulation of enstrophy and kinetic energy at the smallest resolved scales. Horizontal diffusion (other equivalent terms are lateral or scale-selective horizontal damping), therefore, offsets the enstrophy cascade in the free atmosphere and helps to parameterize the dissipation of kinetic energy at unresolved scales ( Tung and Orlando 2003 ). In the

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Richard Rotunno and George H. Bryan

, hereafter BR09b) , using an axisymmetric numerical model with fixed external parameters, conducted a systematic study of the dependence of simulated nearly steady hurricane intensity on the internal modeling parameters. BR09b found the strongest sensitivity of simulated structure and maximum intensity coming from the parameterized diffusion. In the present article, the authors take a closer look at this sensitivity through budget analysis of the BR09b numerical simulations and comparison of these

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C. Liu, Y. Liu, and H. Xu

1. Introduction The evolution of a many-body system like the atmosphere in nonequilibrium involves the irreversible physical processes such as diffusion within the system. A proper description of diffusion is of critical importance for a numerical weather prediction (NWP) model. In the early NWP models ( Cheng 1975 ), the second-order diffusion schemes were, indeed, introduced as a dissipative term similar to viscosity into a prognostic equation. During the 1980s some models progressed to the

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Jason C. Knievel, George H. Bryan, and Joshua P. Hacker

1. Introduction One of the strengths of the Advanced Research core of the Weather Research and Forecasting (WRF) model is its high effective resolution. This results in simulations whose energy spectra begin to decay at shorter wavelengths than do the spectra of simulations by some other numerical weather prediction models ( Skamarock 2004 ). The WRF model’s high effective resolution is achieved partly through the scale-selective diffusion implicit in the model’s advection schemes ( Skamarock

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Olivier Pannekoucke and Laurent Vezard

. Different models exist for correlation matrix and among them, the diagonal assumption in spectral space ( Courtier et al. 1998 ), which leads to homogeneous correlation functions. Amid the heterogeneous correlation models, one can cite the diagonal assumption in wavelet space ( Fisher 2003 ), the recursive filter approach ( Purser et al. 2003a , b ), and the diffusion equation ( Weaver and Courtier 2001 ). The formulation based on the diffusion equation is now considered. It appears that along the

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Xiaogang Wu and Mu Mu

been many studies about THC (e.g. Rahmstorf 2000 ; Marshall et al. 2001 ; Clark et al. 2002 ; Wunsch and Ferrari 2004 ; Dahl et al. 2005 ; Sévellec et al 2007 , among others), and box models are one of useful tools for solving the problems of THC ( Stommel 1961 ; Rooth 1982 ; Welander 1982 ; Whitehead 1995 ; Rahmstorf 1996 , and many others). However, there is a disadvantage that most box models have ignored: the effect of horizontal diffusion (HD), which may arise as a result of

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Tiziano Tirabassi, Daniela Buske, Davidson M. Moreira, and Marco T. Vilhena

1. Introduction The Eulerian approach for modeling the concentration of contaminants in a turbulent flow in the planetary boundary layer (PBL) is widely used in the field of air pollution studies. The simplicity of the K theory of turbulent diffusion has led to the frequent use of this theory as the mathematical basis for simulating air pollution dispersion. Dry deposition refers to the transfer of air pollution (gas and particles) to the ground, where it is removed. The various transfer

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Paul Krause and Juan M. Restrepo

1. Introduction The diffusion kernel filter (DKF) is a particle-based filtering strategy for continuous-time models and discrete-time data. The type of models and observations we focus on here will, in general, have explicit error terms; for example, the error term in the model can represent unresolved physical processes. The statistics of the model and observation error are presumed known. The data assimilation problem is specified in section 2 . The state vector for which an estimator is

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Jongil Han and Hua-Lu Pan

1. Introduction To improve forecast performance, the model physics in the National Centers for Environmental Prediction’s (NCEP) Global Forecast System (GFS) model, the operational medium-range forecast model at NCEP, is under continual development. However, few significant changes to the convection and vertical diffusion schemes have been made since 2001, due to the difficulty of satisfying the concomitant requirement for a careful consideration of interactions among the model physics packages

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Wolfgang Langhans, Juerg Schmidli, and Christoph Schär

to achieve convergence. As a consequence, convection-permitting applications try to handle physically meaningful energy transport at poorly resolved scales, which are affected not only by subgrid turbulent diffusion, but also by implicit and explicit numerical diffusion. Thus, the effective viscosity of the simulated fluid is not necessarily determined by the subgrid turbulent scheme alone, but also by the implicit dissipative properties of the applied numerical discretization scheme ( Piotrowski

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