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

[1] Global Navigation Satellite System (GNSS)-based radio occultation (RO) is a satellite remote sensing technique providing accurate profiles of the Earth’s atmosphere for weather and climate applications. Above about 30km altitude, however, statistical optimization is a critical process for initializing the RO bending angles in order to optimize the climate monitoring utility of the retrieved atmospheric profiles. Here we introduce an advanced dynamic statistical optimization algorithm, which uses bending angles from multiple days of European Centre for Medium-range Weather Forecasts (ECMWF) short-range forecast and analysis fields, together with averaged-observed bending angles, to obtain background profiles and associated error covariance matrices with geographically varying background uncertainty estimates on a daily updated basis. The new algorithm is evaluated against the existing Wegener Center Occultation Processing System version 5.4 (OPSv5.4) algorithm, using several days of simulated MetOp and observed CHAMP and COSMIC data, for January and July conditions. We find the following for the new method’s performance compared to OPSv5.4: 1.) it significantly reduces random errors (standard deviations), down to about half their size, and leaves less or about equal residual systematic errors (biases) in the optimized bending angles; 2.) the dynamic (daily) estimate of the background error correlation matrix alone already improves the optimized bending angles; 3.) the subsequently retrievedrefractivityprofilesandatmospheric(temperature)profilesbenefit by improvederror characteristics,especiallyabove about 30km. Based on theseencouraging results, we work to employ similar dynamic error covariance estimation also for the observed bending angles and to apply the method to full months and subsequently to entire climate data records.

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A new dynamic approach for statistical optimization of GNSS radio occultation bending angles for optimal climate monitoring utility

The International Reference Ionosphere (IRI) project was established jointly by the Committee on Space Research (COSPAR) and the International Union of Radio Science (URSI) in the late sixties with the goal to develop an international standard for the specification of plasma parameters in the Earth’s ionosphere. COSPAR needed such a specification for the evaluation of environmental effects on spacecraft and experiments in space, and URSI for radiowave propagation studies and applications. At the request of COSPAR and URSI, IRI was developed as a data-based model to avoid the uncertainty of theory-based models which are only as good as the evolving theoretical understanding. Being based on most of the available and reliable observations of the ionospheric plasma from the ground and from space, IRI describes monthly averages of electron density, electron temperature, ion temperature, ion composition, and several additional parameters in the altitude range from 60 km to 2000 km. A working group of about 50 international ionospheric experts is in charge of developing and improving the IRI model. Over time as new data became available and new modeling techniques emerged, steadily improved editions of the IRI model have been published. This paper gives a brief history of the IRI project and describes the latest version of the model, IRI-2012. It also briefly discusses efforts to develop a real-time IRI model. The IRI homepage is at http://IRImodel.org.

/pdf/the-international-reference-ionosphere-2012-a-model-of-1o61n09tjl.pdf

The International Reference Ionosphere 2012 – a model of international collaboration

Recent geochemical data from Oman, Newfoundland, and the western United States suggest that long-term oxidation of Ediacaran oceans resulted in progressive depletion of a large dissolved organic carbon (DOC) reservoir and potentially triggered the radiation of acanthomorphic acritarchs, algae, macroscopic Ediacara organisms, and, subsequently, motile bilaterian animals. However, the hypothesized coupling between ocean oxidation and evolution is contingent on the reliability of continuous geochemical and paleontological data in individual sections and of intercontinental correlations. Here we report high-resolution geochemical data from the fossil-rich Doushantuo Formation (635–551 Ma) in South China that confirm trends from other broadly equivalent sections and highlight key features that have not been observed in most sections or have received little attention. First, samples from the lower Doushantuo Formation are characterized by remarkably stable δ13Corg (carbon isotope composition of organic carbon) values but variable δ34SCAS (sulfur isotope composition of carbonate-associated sulfate) values, which are consistent with a large isotopically buffered DOC reservoir and relatively low sulfate concentrations. Second, there are three profound negative δ13Ccarb (carbon isotope composition of carbonate) excursions in the Ediacaran Period. The negative δ13Ccarb excursions in the middle and upper Doushantuo Formation record pulsed oxidation of the deep oceanic DOC reservoir. The oxidation events appear to be coupled with eukaryote diversity in the Doushantuo basin. Comparison with other early Ediacaran basins suggests spatial heterogeneity of eukaryote distribution and redox conditions. We hypothesize that the distribution of early Ediacaran eukaryotes likely tracked redox conditions and that only after ≈551 Ma (when Ediacaran oceans were pervasively oxidized) did evolution of oxygen-requiring taxa reach global distribution.

https://www.pnas.org/content/pnas/105/9/3197.full.pdf

Pulsed oxidation and biological evolution in the Ediacaran Doushantuo Formation

The Horizontal Wind Model (HWM) has been updated in the thermosphere with new observations and formulation changes. These new data are ground-based 630 nm Fabry-Perot Interferometer (FPI) measurements in the equatorial and polar regions, as well as cross-track winds from the Gravity Field and Steady State Ocean Circulation Explorer (GOCE) satellite. The GOCE wind observations provide valuable wind data in the twilight regions. The ground-based FPI measurements fill latitudinal data gaps in the prior observational database. Construction of this reference model also provides the opportunity to compare these new measurements. The resulting update (HWM14) provides an improved time-dependent, observationally based, global empirical specification of the upper atmospheric general circulation patterns and migrating tides. In basic agreement with existing accepted theoretical knowledge of the thermosphere general circulation, additional calculations indicate that the empirical wind specifications are self-consistent with climatological ionosphere plasma distribution and electric field patterns.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2014EA000089

An update to the Horizontal Wind Model (HWM): The quiet time thermosphere

The Jiamusi (JME) radar is the first high-frequency coherent scatter radar independently developed in China. In this study, we investigate the statistical characteristics of the occurrence rate of F-region ionospheric irregularities between 40°N and 65°N geomagnetic latitude by using the Jiamusi radar data from March 2018 to November 2019. Diurnal and seasonal variations in scattering echoes and their dependence on geomagnetic conditions are statistically investigated. It is shown that the local time of the peak echo occurrence rate varies depending on the season, i.e., approximately 20-22.5 magnetic local time (MLT) in summer, 17.5-20.5 MLT in equinox, and 16-17.5 MLT in winter, which is closely associated with the time of sunset. The echo occurrence rate also increases with the enhancement of the geomagnetic index. To further understand the mechanism of these features, we simulate the distribution of the gradient drift instability indicator ([?]n * V E /n) by using the Thermosphere-IonosphereElectrodynamics General Circulation Model (TIEGCM). The analysis results indicate that the gradient drift instability is an important mechanism for irregularities in this region. Key points: 1. Diurnal and seasonal variations in the scatter occurrence rate and their dependence on Kp conditions are statistically analyzed. 2. The distribution of the gradient drift instability indicator ([?]n * V E /n) is simulated by using the TIEGCM. 3. The gradient drift instability is an important mechanism for the high occurrence rate of echoes in the midlatitude region.

https://essopenarchive.org/doi/pdf/10.1002/essoar.10510509.1

Jiuhou Lei

Papers

Statistical characteristics of midlatitude ionospheric F-region backscatter observed by the SuperDARN Jiamusi radar