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

Solar radiation, which varies over multiple temporal scales, modulates remarkably the evolution of the ionosphere. The solar activity dependence of the ionosphere is a key and fundamental issue in ionospheric physics, providing information essential to understanding the variations in the ionosphere and its processes. Selected recent studies on solar activity effects of the ionosphere are briefly reviewed in this report. This report focuses on (1) observations of solar irradiance at X-ray and extreme ultraviolet wavelengths and the outstanding problems of solar proxies, in the view of ionospheric studies, (2) new findings and improved representations of the features of the solar activity dependence of ionospheric key parameters and the corresponding physical processes, (3) possible phenomena in the ionosphere under extremely high and low solar activity conditions that are unique, as indicated by historical solar datasets and the deep solar minimum of solar cycle 23/24, and (4) statistical studies and model simulations of the ionosphere response to solar flares. The above-mentioned studies provide new clues for comprehensively explaining basic processes in the ionosphere and improving the prediction capability of ionospheric models and related applications.

/pdf/solar-activity-effects-of-the-ionosphere-a-brief-review-m2cu7a7833.pdf

Solar activity effects of the ionosphere: A brief review

[1] In this study, we statistically analyze the latitudinal dependence of F2-layer peak electron densities (NmF2) and total electron content (TEC) responses to solar eclipses by using the ionosonde observations during 15 eclipse events from 1973 to 2006 and the GPS TEC observations during six solar eclipse events from 1999 to 2006. We carried out a model study on the latitudinal dependence of eclipse effects on the ionosphere by running a theoretical ionospheric model with the total eclipse occurring at 13 latitudes from 0 Nt o 60N at intervals of 5. Both the observations and simulations show that the NmF2 and TEC responses have the same latitudinal dependence: the eclipse effects on NmF2 and TEC are smaller at low latitudes than at middle latitudes; at the middle latitudes (>40), the eclipse effect decreases with increasing latitude. The simulations show that the smaller NmF2 responses at low latitudes are mainly because of much higher heights of hmF2 at low latitudes and electron density response decreasing rapidly with increasing height. For the eclipse effects at the middle latitudes (>40), the simulations show that the smaller NmF2 or TEC response at higher latitude is mainly ascribed to the larger downward diffusion flux induced by the larger dip angle at this region, which can partly make up for the plasma loss and alleviate the depression of electron density in the F region. The simulated results show that there is an overall decrease in electron temperature throughout the entire height range at the middle latitude, but for the low latitudes the eclipse effect on electron temperature is much smaller at high heights, which is mainly because of the much smaller reduction of photoelectron production rate at its conjugate low heights where only a partial eclipse with small eclipse magnitude occurs.

http://www.igg.cas.cn/xwzx/yjcg/200911/W020091126310555897309.pdf

Latitudinal dependence of the ionospheric response to solar eclipses

The planetary ionospheric storm index, Wp, is de- duced from the numerical global ionospheric GPS-IONEX maps of the vertical total electron content, TEC, for more than half a solar cycle, 1999-2008. The TEC values are ex- tracted from the 600 grid points of the map at latitudes 60 N to 60 S with a step of 5 and longitudes 0 to 345 E with a step of 15 providing the data for 00:00 to 23:00 h of lo- cal time. The local effects of the solar radiant energy are filtered out by normalizing of the TEC in terms of the solar zenith angle at a particular time and the local noon value 0. The degree of perturbation, DTEC, is computed as log of TEC relative to quiet reference median for 27 days prior to the day of observation. The W-index map is generated by segmentation of DTEC with the relevant thresholds specified earlier for foF2 so that 1 or 1 stands for the quiet state, 2 or 2 for the moderate disturbance, 3 or 3 for the moder- ate ionospheric storm, and 4 or 4 for intense ionospheric storm at each grid point of the map. The planetary iono- spheric storm Wp index is obtained from the W-index map as a latitudinal average of the distance between maximum positive and minimum negative W-index weighted by the lat- itude/longitude extent of the extreme values on the map. The threshold Wp exceeding 4.0 index units and the peak value Wpmax 6.0 specify the duration and the power of the plan- etary ionosphere-plasmasphere storm. It is shown that the occurrence of the Wp storms is growing with the phase of the solar cycle being twice as much as the number of the magnetospheric storms with Dst 100 nT andAp 100 nT.

/pdf/derivation-of-a-planetary-ionospheric-storm-index-5c0bvcd6r4.pdf

Derivation of a planetary ionospheric storm index

The mapping function is commonly used to convert slant to vertical total electron content (TEC) based on the assumption that the ionospheric electrons concentrate in a layer. The height of the layer is called ionospheric effective height (IEH) or shell height. The mapping function and IEH are generally well understood for ground-based global navigation satellite system (GNSS) observations, but they are rarely studied for the low earth orbit (LEO) satellite-based TEC conversion. This study is to examine the applicability of three mapping functions for LEO-based GNSS observations. Two IEH calculating methods, namely the centroid method based on the definition of the centroid and the integral method based on one half of the total integral, are discussed. It is found that the IEHs increase linearly with the orbit altitudes ranging from 400 to 1400 km. Model simulations are used to compare the vertical TEC converted by these mapping functions and the vertical TEC directly calculated by the model. Our results illustrate that the F&K (Foelsche and Kirchengast) geometric mapping function together with the IEH from the centroid method is more suitable for the LEO-based TEC conversion, though the thin layer model along with the IEH of the integral method is more appropriate for the ground-based vertical TEC retrieval.

Assessment of vertical TEC mapping functions for space-based GNSS observations

Using 8-year global ionosphere maps (GIMs) of TEC products from the Jet Propulsion Laboratory (JPL), we make a statistical study on the morphology of the global ionospheric behaviors with respect to the geomagnetic disturbances. Results show that the behaviors of TEC during geomagnetic storm present clear seasonal and local time variations under geomagnetic control in a similar way as those of NmF2 (Field and Rishbeth, 1997). A negative phase of TEC occurs with high probability in the summer hemisphere and most prominent near the geomagnetic poles, while a positive phase is obvious in the winter hemisphere and in the far pole region. A negative storm effect toward lower latitudes tends to occur from post-midnight to the morning sector and recedes to high latitude in the afternoon. A positive storm effect is separated by geomagnetic latitudes and magnetic local time. Furthermore, ionospheric responses at different local time sectors with respect to the storm commencement shows very different developing processes corresponding to the evolution of the geomagnetic storm. A daytime positive storm effect is shown to be more prominent in the American region than those in the Asian and European regions, which may suggest a longitudinal effect of the ionospheric storm.

https://angeo.copernicus.org/articles/25/1555/2007/angeo-25-1555-2007.pdf

Morphology in the total electron content under geomagnetic disturbed conditions: results from global ionosphere maps

In this paper, winds derived from OH Meinel 892.0 nm detection by an FPI (Fabry-Perot Interferometer) are compared with the simultaneous wind measurements from a meteor radar during April–May of 2010. The peak height of OH Meinel 892.0 nm is about 87 km. The variations of FPI wind at 87 km mostly have the similar track to meteor radar wind at 87 km, and the data values of FPI wind mainly fall into the range of meteor radar wind. However, there are still quantitative differences between the observations of the two systems. The best cross-correlation occurs in meridional winds from two systems in April of 2010. An obvious wave signal with 0.2 cycle/d frequency is found in meridional winds observed by both FPI and meteor radar.

A comparison of mesospheric winds measured by FPI and meteor radar located at 40N

In this paper, we calculate the ionospheric global electron content (GEC) from the GPS TEC data along the geographic longitude 120 degrees E during the period of 1996-2004, and investigate the relationship between GEC and 10.7 cm solar radio flux F-10.7 and its seasonal dependence with partial correlation analysis. Our results show that GEC is closely correlated with solar activity index F-10.7 and is also related with annual and semiannual variations. An empirical GEC model driven by those factors is then to examine the influences of different solar activity proxies for the model input. The results suggest that GEC mainly depends on solar activity and the seasonal variations; the latter is also modulated by solar activity. Furthermore, the magnitude of semiannual variation is a little greater than that of annual variation. Our empirical GEC model is proved to be better than the model proposed by Afraimovich et al.

Climatological analysis and modeling of the ionospheric global electron content

On the basis of a multiple linear regression model performed for ionospheric NmF2, partial correlation method is first applied to investigating the relation between NmF2 and h (the height of isobaric level) in the lower atmosphere over Wuhan, China during 1957–2004. The results show that partial correlation method can eliminate the influences of solar and geomagnetic activities as well as the seasonal variation factors and reveal the true correlation between NmF2 and h in the lower atmosphere. A weak positive correlation between NmF2 and h is found in the middle stratosphere. In addition, by comparing the partial correlation coefficients between NmF2 and its influence factors, we find that NmF2 is mainly affected by solar activity and the seasonal variation factors, and weakly affected by geomagnetic activity, but hardly affected by h in the lower atmosphere. The study suggests that partial correlation method is a helpful tool for investigating the correlation between ionospheric parameter and its influence factors.

Applying partial correlation method to analyzing the correlation between ionospheric NmF2 and height of isobaric level in the lower atmosphere

An attempt is made to estimate the plasmaspheric electron content (PTEC) using the data observed from the ISR (Incoherent Scatter Radar) and GPS at Millstone Hill (42. 6 degrees N, 288. 5 degrees E). We first present a brief description on the method we used in this study, then the variation of PTEC is studied. The electron density profile obtained by the ISR at Millstone Hill is fitted using Chapman function with varying scale heights, and then the ISR TEC is calculated as an integral of electron density from 100km to 1000km of the profile. The difference between GPS TEC (which is up to an altitude of 20200 km) and ISR TEC can be taken approximately as the plasmaspheric electron content (PTEC). Data from both high solar activity years (2000 and 2002) and low solar activity years (2005 and 2008) are used for the present study. The results we obtained indicate that both PTEC and the relative contribution of PTEC (to GPSTEC) exhibit obvious diurnal variation patterns, with PTEC being higher during daytime than during nighttime and the relative contribution of PTEC is higher during nighttime than during daytime. PTEC can vary from 4 to 14 TECU (1TECU = 10(16)el/m(2)) and the contribution of PTEC to GPS TEC reaches 60% during nighttime in the month of high solar activity level, while in the month of low solar activity, the value of PTEC is generally 3 similar to 7 TECU with the highest contribution about 80% at night. The variation pattern and trends in our results are in agreement with those obtained by other researches based on different measurements and techniques, and the magnitude is also agreed. This provides a support to the validity of our method. Unlike the ionosonde/digisonde which can only explore the bottomside ionosphere under the F2 peak, the ISR has the advantage to explore from a low to high altitude range and thus can provide both the bottomside and topside electron density profile. For this reason, the PTEC derived from ISR data (combined with GPS TEC) is more realistic than that from ionosonde data (combined with GPS TEC). This latter approach was often adopted by some former researchers.

Wan Weixing

Papers

Morphology in the total electron content under geomagnetic disturbed conditions: results from global ionosphere maps

A comparison of mesospheric winds measured by FPI and meteor radar located at 40N

Climatological analysis and modeling of the ionospheric global electron content

Applying partial correlation method to analyzing the correlation between ionospheric NmF2 and height of isobaric level in the lower atmosphere

An investigation on plasmaspheric electron content derived from ISR and GPS observations at Millstone Hill