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

“Best tracks” are National Hurricane Center (NHC) poststorm analyses of the intensity, central pressure, position, and size of Atlantic and eastern North Pacific basin tropical and subtropical cyclones. This paper estimates the uncertainty (average error) for Atlantic basin best track parameters through a survey of the NHC Hurricane Specialists who maintain and update the Atlantic hurricane database. A comparison is then made with a survey conducted over a decade ago to qualitatively assess changes in the uncertainties. Finally, the implications of the uncertainty estimates for NHC analysis and forecast products as well as for the prediction goals of the Hurricane Forecast Improvement Program are discussed.

Atlantic Hurricane Database Uncertainty and Presentation of a New Database Format

Since its initial release in 2000, the Weather Research and Forecasting (WRF) Model has become one of the world’s most widely used numerical weather prediction models. Designed to serve both research and operational needs, it has grown to offer a spectrum of options and capabilities for a wide range of applications. In addition, it underlies a number of tailored systems that address Earth system modeling beyond weather. While the WRF Model has a centralized support effort, it has become a truly community model, driven by the developments and contributions of an active worldwide user base. The WRF Model sees significant use for operational forecasting, and its research implementations are pushing the boundaries of finescale atmospheric simulation. Future model directions include developments in physics, exploiting emerging compute technologies, and ever-innovative applications. From its contributions to research, forecasting, educational, and commercial efforts worldwide, the WRF Model has made a s...

The Weather Research and Forecasting Model: Overview, System Efforts, and Future Directions

Sea salt aerosol (SSA) exerts a major influence over a broad reach of geophysics. It is important to the physics and chemistry of the marine atmosphere and to marine geochemistry and biogeochemistry generally. It affects visibility, remote sensing, atmospheric chemistry, and air quality. Sea salt aerosol particles interact with other atmospheric gaseous and aerosol constituents by acting as sinks for condensable gases and suppressing new particle formation, thus influencing the size distribution of these other aerosols and more broadly influencing the geochemical cycles of substances with which they interact. As the key aerosol constituent over much of Earth's surface at present, and all the more so in pre-industrial times, SSA is central to description of Earth's aerosol burden.

Sea Salt Aerosol Production: Mechanisms, Methods, Measurements, and Models - A Critical Review

The future impacts of climate change on landfalling tropical cyclones are unclear. Regardless of this uncertainty, flooding by tropical cyclones will increase as a result of accelerated sea-level rise. Under similar rates of rapid sea-level rise during the early Holocene epoch most low-lying sedimentary coastlines were generally much less resilient to storm impacts. Society must learn to live with a rapidly evolving shoreline that is increasingly prone to flooding from tropical cyclones. These impacts can be mitigated partly with adaptive strategies, which include careful stewardship of sediments and reductions in human-induced land subsidence.

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Coastal flooding by tropical cyclones and sea-level rise

Observations of wind profiles within the tropical cyclone boundary layer have until recently been quite rare. The recent massive increase in observations due to the operational implementation of the global positioning system dropwindsonde has emphasised that a low-level wind speed maximum is a common feature of the tropical cyclone boundary layer. Here is proposed a mechanism for producing such a maximum, whereby strong inward advection of angular momentum generates the supergradient flow. The processes that maintain the necessary inflow against the outward acceleration resulting from gradient wind imbalance are identified as being (i) vertical diffusion, (ii) vertical advection, and (iii) horizontal advection. Two complementary tools are used to diagnose the properties and dynamics of the jet. The first, presented here, is a linear analytical model of the boundary layer flow in a translating tropical cyclone. It is an extension of the classical Ekman boundary layer model, as well as of earlier w...

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The Dynamics of Boundary Layer Jets within the Tropical Cyclone Core. Part I: Linear Theory

Observations of wind profiles within the tropical cyclone boundary layer until recently have been quite rare. However, the recent spate of observations from the GPS dropsonde have confirmed that a low-level wind speed maximum is a common feature of the tropical cyclone boundary layer. In Part I, a mechanism for producing such a maximum was proposed, whereby strong inward advection of angular momentum generates the supergradient flow. The processes that maintain the necessary inflow against the outward acceleration due to gradient wind imbalance were identified as being (i) vertical diffusion, (ii) vertical advection, and (iii) horizontal advection, and a linear analytical model of the boundary layer flow in a translating tropical cyclone was presented and used to diagnose the properties of the jet and the near-surface flow. A significant shortcoming was that the jet was too weak, which was argued to be due to the neglect of vertical advection. Here, a high-resolution, dry, hydrostatic, numerical ...

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The Dynamics of Boundary Layer Jets within the Tropical Cyclone Core. Part II: Nonlinear Enhancement

The boundary layer in a tropical cyclone is in some respects unlike that elsewhere in the atmosphere. It is therefore necessary to evaluate boundary layer parameterizations for their suitability for use in tropical cyclone simulation. Previous work has shown substantial sensitivity to the choice of scheme and identified specific shortcomings in some schemes, but without recommending which schemes are most suitable. Here, several schemes, representative of those available in popular modeling systems, are reviewed and applied in a simplified modeling framework. Based on a comparison with observations and on theoretical grounds, one popular class of schemes is shown to be badly flawed in that it incorrectly predicts the near-surface wind profile, and therefore should not be used. Another is shown to be sensitive to diagnosis of the boundary layer depth, a difficult problem in the core of the tropical cyclone, and caution is advised. The Louis boundary layer scheme and a higher-order closure scheme ar...

https://journals.ametsoc.org/doi/pdf/10.1175/MWR-D-11-00217.1

Choosing a Boundary Layer Parameterization for Tropical Cyclone Modeling

The GPS dropsonde allows observations at unprecedentedly high horizontal and vertical resolution, and of very high accuracy, within the tropical cyclone boundary layer. These data are used to document the boundary layer wind field of the core of Hurricane Georges (1998) when it was close to its maximum intensity. The spatial variability of the boundary layer wind structure is found to agree very well with the theoretical predictions in the works of Kepert and Wang. In particular, the ratio of the near-surface wind speed to that above the boundary layer is found to increase inward toward the radius of maximum winds and to be larger to the left of the track than to the right, while the low-level wind maximum is both more marked and at lower altitude on the left of the storm track than on the right. However, the expected supergradient flow in the upper boundary layer is not found, with the winds being diagnosed as close to gradient balance. The tropical cyclone boundary layer model of Kepert and Wan...

Observed Boundary Layer Wind Structure and Balance in the Hurricane Core. Part I: Hurricane Georges

A major limitation of the Ensemble Kalman Filter (EnKF) is that the finite ensemble size introduces sampling error into the background covariances, with severe consequences for atmospheric and oceanographic applications. The negative effects of sampling error are customarily limited by covariance localisation, which earlier studies have suggested may introduce imbalance into the system. The deleterious effects of localisation upon balance are confirmed and detailed here, with localisation producing analyses with weaker geostrophic balance and stronger divergence than are obtained using the unlocalised covariances. These imbalances reduce as the localisation radius is increased, but are argued to be large for typical settings. An improved method for calculating local covariances from an ensemble is presented, in which the localisation is performed in streamfunction–velocity potential (ψ–χ), rather than wind component, space. Analyses using this method better preserve the balances contained within the unlocalised covariance model. This transformation further allows the option of intervariable localisation, in which the cross-covariances involving χ, which are weak and therefore particularly subject to sampling error, are set to 0 instead of being calculated from the ensemble. The various localisations are compared in a series of identical-twin experiments, with the new localisations producing analyses that are better balanced and significantly more accurate than the usual approach. The localisation with the χ cross-covariances set to 0 is shown to be superior for the smaller ensemble sizes but not for the larger, implying that the larger ensembles are capable of resolving some of the true χ cross-covariance in the test system. Copyright © 2009 Royal Meteorological Society

Jeffrey D. Kepert

Papers

The Dynamics of Boundary Layer Jets within the Tropical Cyclone Core. Part I: Linear Theory

The Dynamics of Boundary Layer Jets within the Tropical Cyclone Core. Part II: Nonlinear Enhancement

Choosing a Boundary Layer Parameterization for Tropical Cyclone Modeling

Observed Boundary Layer Wind Structure and Balance in the Hurricane Core. Part I: Hurricane Georges

Covariance localisation and balance in an Ensemble Kalman Filter