The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

This chapter assesses long-term projections of climate change for the end of the 21st century and beyond, where the forced signal depends on the scenario and is typically larger than the internal variability of the climate system. Changes are expressed with respect to a baseline period of 1986-2005, unless otherwise stated.

Chapter 12 - Long-term climate change: Projections, commitments and irreversibility

This comprehensive text and reference work on numerical weather prediction, first published in 2002, covers not only methods for numerical modeling, but also the important related areas of data assimilation and predictability. It incorporates all aspects of environmental computer modeling including an historical overview of the subject, equations of motion and their approximations, a modern and clear description of numerical methods, and the determination of initial conditions using weather observations (an important science known as data assimilation). Finally, this book provides a clear discussion of the problems of predictability and chaos in dynamical systems and how they can be applied to atmospheric and oceanic systems. Professors and students in meteorology, atmospheric science, oceanography, hydrology and environmental science will find much to interest them in this book, which can also form the basis of one or more graduate-level courses.

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Atmospheric Modeling, Data Assimilation and Predictability

Description of the NCAR Community Atmosphere Model (CAM 3.0)

(2005). Atmospheric Modeling, Data Assimilation, and Predictability. Technometrics: Vol. 47, No. 4, pp. 521-521.

Atmospheric Modeling, Data Assimilation, and Predictability

The steady-state extratropical atmospheric response to thermal forcing is investigated in a simple atmospheric general circulation model. The thermal forcings qualitatively mimic three key aspects of anthropogenic climate change: warming in the tropical troposphere, cooling in the polar stratosphere, and warming at the polar surface. The principal novel findings are the following: 1) Warming in the tropical troposphere drives two robust responses in the model extratropical circulation: poleward shifts in the extratropical tropospheric storm tracks and a weakened stratospheric Brewer–Dobson circulation. The former result suggests heating in the tropical troposphere plays a fundamental role in the poleward contraction of the storm tracks found in Intergovernmental Panel on Climate Change (IPCC)-class climate change simulations; the latter result is in the opposite sense of the trends in the Brewer–Dobson circulation found in most previous climate change experiments. 2) Cooling in the polar stratosp...

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The Steady-State Atmospheric Circulation Response to Climate Change–like Thermal Forcings in a Simple General Circulation Model

The streamfunction-velocity potential form of shallow-water equations, implemented on a spherical geodesic grid, offers an attractive solution to many of the problems associated with fluid-flow simulations in a spherical geometry. Here construction of a new type of spherical geodesic grid is outlined, and discretization of the equations is explained. The model is subjected to the NCAR suite of seven test cases for shallow-water models.

Numerical Integration of the Shallow-Water Equations on a Twisted Icosahedral Grid. Part I: Basic Design and Results of Tests

The finite-difference scheme for the Laplace and flux-divergence operators described in the companion paper (Part I) is consistent when applied on a grid consisting of perfect hexagons. The authors describe a necessary and sufficient condition for this finite-difference scheme to be consistent when applied on a grid consisting of imperfect hexagons and pentagons, and present an algorithm for generating a spherical geodesic grid on a sphere that guarantees that this condition is satisfied. Also, the authors qualitatively describe the error associated with the operators and estimate their order of accuracy when applied on the new grid.

Numerical Integration of the Shallow-Water Equations on a Twisted Icosahedral Grid. Part II. A Detailed Description of the Grid and an Analysis of Numerical Accuracy

A new approach to climate simulation uses geodesic grids generated from an icosahedron and could become on attractive alternative to current models We implemented an atmospheric general circulation model using a geodesic discretization of the sphere Our model uses the message-passing interface and runs efficiently on massively parallel machines

Climate modeling with spherical geodesic grids

This paper documents the development and testing of a new type of atmospheric dynamical core. The model solves the vorticity and divergence equations in place of the momentum equation. The model is discretized in the horizontal using a geodesic grid that is nearly uniform over the entire globe. The geodesic grid is formed by recursively bisecting the triangular faces of a regular icosahedron and projecting those new vertices onto the surface of the sphere. All of the analytic horizontal operators are reduced to line integrals, which are numerically evaluated with second-order accuracy. In the vertical direction the model can use a variety of coordinate systems, including a generalized sigma coordinate that is attached to the top of the boundary layer. Terms related to gravity wave propagation are isolated and an efficient semi-implicit time-stepping scheme is implemented. Since this model combines many of the positive attributes of both spectral models and conventional finite-difference models in...

Ross Heikes

Papers

The Steady-State Atmospheric Circulation Response to Climate Change–like Thermal Forcings in a Simple General Circulation Model

Numerical Integration of the Shallow-Water Equations on a Twisted Icosahedral Grid. Part I: Basic Design and Results of Tests

Numerical Integration of the Shallow-Water Equations on a Twisted Icosahedral Grid. Part II. A Detailed Description of the Grid and an Analysis of Numerical Accuracy

Climate modeling with spherical geodesic grids

Modeling the Atmospheric General Circulation Using a Spherical Geodesic Grid: A New Class of Dynamical Cores