Ionospheric dynamics and drivers obtained from a physics-based data assimilation model

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1 RADIO SCIENCE, VOL. 44,, doi: /2008rs004068, 2009 Ionospheric dynamics and drivers obtained from a physics-based data assimilation model Ludger Scherliess, 1 Donald C. Thompson, 1 and Robert W. Schunk 1 Received 28 October 2008; revised 29 May 2009; accepted 13 July 2009; published 30 September [1] The ionosphere-plasmasphere system at low and middle latitudes is strongly coupled, and therefore, a study of ionospheric dynamics must take into account the interaction between the two domains. As shown by meteorologists and oceanographers, a powerful way of modeling dynamic systems is with the use of data assimilation models. At Utah State University, we have developed two data assimilation models with different complexity, and both provide global and regional specifications of the three-dimensional (3-D) ionosphere-plasmasphere densities. One of these models is a Full Physics-Based Kalman filter data assimilation model, which is based on a physics-based model for the ionosphere-plasmasphere system, a diverse array of data sources, and an ensemble Kalman filter data assimilation technique. This model covers the ionosphere-plasmasphere system from 90 to 30,000 km altitude and includes six ion species (NO +,N + 2,O + 2,O +,He +, H + ). The strength of this model is that in addition to the global and regional 3-D ionosphere electron density distribution it also self-consistently determines the corresponding ionospheric drivers, including the thermospheric neutral winds and the lowlatitude electric fields. The model can assimilate a variety of different data types, including GPS/total electron content from hundreds of ground-based receivers, in situ N e from several DMSP satellites, bottomside N e profiles from tens of ionosondes, and occultation data from the six COSMIC satellites. In this study, the model was used to specify the lowlatitude and midlatitude ionosphere together with the ionospheric driving forces and their temporal and spatial variability. Citation: Scherliess, L., D. C. Thompson, and R. W. Schunk (2009), Ionospheric dynamics and drivers obtained from a physics-based data assimilation model, Radio Sci., 44,, doi: /2008rs Introduction [2] The midlatitude and low-latitude ionospherethermosphere system varies markedly with altitude, latitude, longitude, universal time, season, solar cycle, and geomagnetic activity. The primary driving mechanism for the ionosphere-thermosphere system is solar ultraviolet (UV) and extreme ultraviolet (EUV) radiation, which affects ionization, temperatures and neutral winds. The subsequent interaction of the ionosphere, thermosphere and the Earth s magnetic field drives electric fields, which feed back into the ionosphere-thermosphere structure. Furthermore, during geomagnetically disturbed times, electric fields penetrating from the high latitudes toward the lower latitudes, storm-induced neutral winds, 1 Center for Atmospheric and Space Sciences, Utah State University, Logan, Utah, USA. Copyright 2009 by the American Geophysical Union /09/2008RS and changes in the neutral composition also affect the low-latitude and midlatitude plasma dynamics and can create dramatic responses in the ionosphere. As a result the low-latitude and midlatitude ionosphere exhibits a significant amount of dynamics during both geomagnetically quiet and disturbed conditions. [3] At middle latitudes, storm-enhanced plasma densities (SEDs) are frequently observed during periods of enhanced geomagnetic activity. These bands of largely increased density structures, often extending from Florida over the Great Lakes region into central Canada, are believed to be caused by storm time electric fields that transport plasma from low to middle latitudes [Foster et al., 2002; Coster et al., 2003]. However, the midlatitude ionosphere exhibits a significant amount of variability even during geomagnetically quiet times due to spatial and temporal variations in the electric field and the neutral wind and composition. [4] At low latitudes the daytime upward E x B plasma drift near the dip equator and parallel motion down the 1of8

2 field lines creates the equatorial ionization anomaly. The largest densities and total electron content (TEC) values occur in the ionization anomaly peaks. Recently, Immel et al. [2006] presented Imager for Magnetopause-to- Aurora Global Exploration (IMAGE) far ultraviolet (FUV) observations of the nm recombination airglow between 2030 and 2200 LT that show a fourcell longitude pattern in the brightness at the crests of the equatorial anomaly. This four-cell pattern has been attributed to the E region dynamo winds associated with the nonmigrating, eastward propagating, wave number 3 diurnal tide (DE3) [Hagan and Forbes, 2002]. However, a significant amount of scatter remains in the lowlatitude ionosphere that is not accounted for by this tidal modulation [Scherliess et al., 2008]. The remaining variability (ionospheric weather) is found to be of the order of 40% and is believed to be caused by variations in the electric field, and neutral wind and composition. [5] Ionospheric weather and its associated structures, gradients and variability has large impacts on a variety of technological systems and can strongly affect navigation, communication, and radar operations. Over the past decades numerous analytical, parameterized, and global physics-based models have been developed in an effort to better understand and specify ionospheric weather. In addition, coupled models that combine different spatial domains have been developed and a review of recent model developments is given by Schunk et al. [2002]. Although physics-based models of the ionosphere reproduce many of the observed climatological features, these models generally fail to specify ionospheric weather. This lack of reliable specifications is largely attributed to a lack of reliable specifications of the ionospheric drivers, which include the thermospheric composition and winds, the equatorial and high-latitude electric fields and the high-latitude particle precipitation. Currently, the most promising models for ionospheric weather specification are data assimilation models that combine physics-based models of the ionosphere with observations. Data assimilation models have been used extensively over the past decades in meteorology and oceanography for specifications and forecasts [Daley, 1991] and are now also being used for ionospheric studies [e.g., Hajj et al., 2004; Scherliess et al., 2004, 2006a; Angling and Khattatov, 2006]. Recently we have developed a physicsbased data assimilation model for the ionosphere that is based on a physics-based model of the ionosphere plasmasphere system and an ensemble Kalman filter technique. One of the main advantages of this model is that in addition to its specification of the ionospheric plasma densities it also provides the self-consistent specification for the ionospheric driving forces. In what follows, this new model will be briefly described and first results will be shown. In the following sections, we will first describe our new physics-based data assimilation model and then show example results obtained from this model at low latitudes and midlatitudes. 2. Physics-Based Data Assimilation Models [6] At Utah State University, we have developed two physics-based Kalman filter data assimilation models for the near-earth space environment. The two models are the Gauss-Markov Kalman Filter Model (GAIM-GM) and the Full Physics-Based Kalman Filter Model (GAIM-FP) [Schunk et al., 2004, 2005; Scherliess et al., 2004, 2006a; McDonald et al., 2006; Thompson et al., 2006, 2009; Sojka et al., 2007; Jee et al., 2007, 2008]. Both models are part of the Global Assimilation of Ionospheric Measurements (GAIM) project. Our Gauss-Markov Kalman filter model is a simpler model that can be run on one Central Processing Unit (CPU) and provides the global electron density distribution. Recently, the accuracy of this model for global and regional ionospheric specifications has been shown by Scherliess et al. [2006a], Thompson et al. [2006], Sojka et al. [2007], and independently by Decker and McNamara [2007], McNamara et al. [2007, 2008], and McDonald et al. [2006]. These studies have concluded that our Gauss-Markov Kalman filter model is well suited to accurately capture the electron density distribution and its variations in the global ionosphere. The Gauss-Markov Kalman filter model uses a statistical (Gauss-Markov) process to evolve the Kalman filter state (plasma density perturbations) and state error covariances in time [Scherliess et al., 2006a, 2006b]. Our Full Physics-Based Kalman filter model, on the other hand, is a sophisticated data assimilation model that uses a physics-based ionosphere-plasmasphere model and an ensemble Kalman filter technique to incorporate the ionospheric production, loss, and transport processes directly into the data assimilation scheme. This should provide a much more realistic evolution of the plasma density distribution and the state error covariance. In addition, the model provides self-consistent distributions of the ionospheric drivers (electric field, neutral wind, and composition) at low latitudes and midlatitudes. The determination and subsequent feedback of these drivers into the data assimilation model should provide a much improved altitude structure of the low-latitude and midlatitude plasma distribution. In particular should the height of the F2 region (hmf2) be largely improved when compared to the Gauss-Markov Kalman filter model. This latter model lacks this driver estimation and feedback. Both models can assimilate a diverse set of measurements and some of the data that we have already assimilated in our data assimilation models include in situ electron density measurements from four Defense Meteorological Satellite Program (DMSP) satellites, bottomside electron density profiles from 2of8

3 30 ionosondes, TEC data from a network of up to 1000 global positioning system (GPS) ground stations, ultraviolet (UV) radiances from the SSUSI, SSULI, and LORAAS instruments, and radio occultation data from the CHAMP, SAC-C, IOX, and COSMIC satellites. The Full Physics-Based data assimilation model provides specifications on a spatial grid that can be global, regional, or local and its output includes the threedimensional electron and ion (NO +,O 2 +,N 2 +,O +,H +, He + ) density distributions from 90 km to geosynchronous altitude (30,000 km). As mentioned above, the model also provides the self-consistent distributions of the ionospheric drivers (electric field, neutral wind, and composition) at low latitudes and midlatitudes. In the following sections, our full physics-based data assimilation model is briefly discussed Full Physics-Based Data Assimilation Model [7] The Full Physics-Based Kalman Filter Model uses an ensemble Kalman filter approach and rigorously evolves the ionosphere and plasmasphere electron density field and its associated errors using a physical model of the ionosphere/plasmasphere system [Schunk et al., 2004, 2005; Scherliess et al., 2004, 2006b] that covers low latitudes and midlatitudes. The data assimilation model excludes, in its current version, geomagnetic latitudes poleward of ±60 geomagnetic latitude due to the vastly different physical processes that govern the high-latitude regions, e.g., convection electric fields, particle precipitation, etc. The physics-based model and the ensemble Kalman filter technique are described in what follows Ionosphere-Plasmasphere Model [8] The Ionosphere-Plasmasphere Model (IPM) [Schunk et al., 2004; Scherliess et al., 2004] is a threedimensional, high-resolution, multi-ion model of the ionosphere-plasmasphere system that covers the altitude range from 90 to 30,000 km. The IPM is based on a numerical solution of the ion and electron continuity and momentum equations [Schunk and Nagy, 2000]. The model calculates three-dimensional, time-dependent, density distributions for four major ions (NO +,O + 2,N + 2, O + )ateregion altitudes and three major ions (O +,H +,He + ) in the F region and plasmasphere. The equations are solved along magnetic field lines for individual convecting flux tubes of plasma, and the 3-D nature of the model is obtained by following a large number of plasma flux tubes. The IPM uses the International Geomagnetic Reference Field (IGRF), which properly accounts for the displacement between the geomagnetic and geographic equators and the bending of the B field lines with latitude. These features are important at low latitudes and midlatitudes. The inclusion of He + as a major ion is also important because, at Arecibo, it is 3of8 frequently observed to be a dominant ion in a distinct altitude range [González and Sulzer, 1996]. In the plasmasphere He + is also important and can account for up to 30% of the plasmaspheric material. The spatial resolution of the IPM along magnetic field lines is about 1kmatE and F region altitudes, 4 km in the topside ionosphere, and 240 km at an altitude of 17,000 km. In order to resolve mesoscale plasma density structures and their steep gradients often observed in the midlatitude and low-latitude regions, the horizontal resolution of the model is fully flexible and can be adjusted to capture these structures. Note that it is important for the proper interpretation of ground-based GPS/TEC data that our modeling effort also includes the plasmasphere [Thompson et al., 2009]. The ground-based GPS/TEC is an integral of the electron density along the slant path from the ground receiver to the GPS satellite (at about 20,000 km). At midlatitudes and low latitudes the GPS path traverses through the entire plasmasphere and the plasmaspheric contribution to TEC can exceed 50% at night [Lunt et al., 1999] Ensemble Kalman Filter [9] The Kalman filter is a well documented technique that can be derived as a recursive algorithm that minimizes the error (i.e., finds the best estimate of the state) at a time t based on all information prior to this time [Daley, 1991]. The goal is to combine the measurement data from an actual observing system with the information obtained from the system model and their corresponding statistical description of uncertainties. Formally, the filter performs a recursive least squares inversion of the observations (e.g., electron density profiles, line-of-sight TEC, etc.) for the model variables using a dynamical model as a constraint. In practice, a weighted average of the model estimate and data is performed, using the relative accuracy of the two as the weights. As a result, an improved estimate of the model variables is obtained, where the improvement is in a statistical sense, i.e., it has the least expected error given the observations, the model, and their error statistics. In this approach, the specification of the error covariances for both the model and the observations is of crucial importance. The data error covariance generally consists of two parts, one part associated with the observational error and the second part associated with the representativeness of the observations and both parts are currently only vaguely known. For example, are possible correlations in the data errors in the current model not been taken into account. The system model, which provides the temporal evolution of both the state vector and the model error covariance matrix, is in our case the physics-based ionosphereplasmasphere model (IPM). Along with the best estimate of the state, the Kalman filter also generates a theoretical estimate of the analysis error.

4 [10] Although it is, in principle, straightforward to apply the Kalman filter, difficulties arise when implementing the filter due to the enormous computational requirements, both in storage and CPU time, associated with the propagation of the model error covariance matrix. In addition, the typically required linearization of the physical model, which can be done numerically, is very time-consuming and is an additional source of error. Therefore, as a practical method, an ensemble Kalman filter can be used to calculate the state error covariance matrix [Evensen, 2003]. This approximation leads to a dramatic reduction in the computational requirements and also eliminates the time-consuming numerical linearization of the model. Instead, the full nonlinear physical model can be used. [11] Over the past decade, the ensemble Kalman filter has been successfully employed in meteorological and oceanographic data assimilation. The ensemble Kalman filter is a sequential data assimilation method that uses a Monte Carlo or ensemble integration. By integrating an ensemble of model states forward in time, it is possible, using standard statistical techniques, to calculate the mean state and the error covariances needed at the analysis time. In our case, tests with different numbers of ensemble members indicate that about 30 model runs are needed. Note that these 30 model runs are launched at each assimilation time step, and as time proceeds, the Kalman filter converges to the optimum combination of error covariances, N e distributions, model drivers, and data. The number of ensemble members in the model is, however, fully flexible and can easily be adjusted. [12] It is important to note that the estimation of the ionospheric drivers is an integral part of our ensemble Kalman filter and is achieved by using the internal physics-based model sensitivities to the various driving forces. In this procedure, the ionospheric data are used to adjust the plasma densities and its drivers so that a consistency between the observations (within their errors) and the physical model is achieved. As a result the assimilation procedure produces the optimal modeldata combination of the ionosphere-plasmasphere system with its self-consistent drivers (electric fields and neutral winds and composition). 3. Full Physics-Based Kalman Filter Examples [13] In the following, we will show example results from our full physics-based data assimilation model for two 4-day long runs in March 2004 and April During these periods the model assimilated a variety of different data types and specified the ionospheric plasma density and its drivers on a global scale from ±60 magnetic latitude. Although the model results are for 4of8 both periods available over this entire domain, we will in the following separately address the midlatitude and lowlatitude responses using the March 2004 and the April 2007 periods, respectively Midlatitude Kalman Filter Example [14] In the first example, we will show the ionospheric and neutral wind specifications at midlatitudes obtained from the Full Physics-Based Kalman Filter Model. In this example, the model was used to study the ionospheric and thermospheric variability during a 4-day period (20 23 March 2004). During this geomagnetically quiet period, the model assimilated in situ electron densities from 2 DMSP satellites (F13, F15), bottomside electron density profiles from several globally distributed ionosondes, and slant TEC from a network of more than 200 GPS ground receivers. The data were continuously assimilated throughout the 4-day period and the physicsbased Kalman filter produced a 3-D reconstruction of the ionosphere and plasmasphere. The reconstruction covered all longitudes, magnetic latitudes between 60 S and 60 N, and altitudes from 90 to 20,000 km. [15] Figure 1a shows a snapshot of the TEC distribution as a function of latitude and longitude over the North American continent (where the data coverage was most dense). The vertical TEC was obtained by integrating through the 3-D ionosphere-plasmasphere from 90 km to the upper boundary. For comparison, Figure 1c shows the TEC obtained from the ionosphere-plasmasphere model without assimilating the data. Note the large difference between the two TEC maps. As mentioned above, the Full Physics-Based Kalman Filter Model is also capable of estimating the ionospheric drivers. Figure 1b shows the meridional wind obtained from our data assimilation model. For comparison the meridional neutral wind obtained from the Horizontal Wind Model (HWM) [Hedin et al., 1996] is shown in Figure 1d. A comparison of the physics-based Kalman filter electron density reconstruction with measurements not included in the data assimilation scheme indicates that the physics-based Kalman filter model is able to satisfactorily specify the ionospheric N e distribution. Note that although our neutral wind specifications at midlatitudes could include an electric field component, the effect of this electric field is believed to be small during geomagnetically quiet periods. [16] The differences between the assimilation results and the climatological specifications become even more dramatic when the day-to-day variations of the ionospheric densities and the neutral winds are compared. Figure 2 shows, as an example, the temporal evolution of TEC (Figure 2, top) and of the meridional neutral wind (Figure 2, bottom) over Wallops Island (38 N, 75 W) for the 4-day period. The TEC values shown in Figure 2 (top) were obtained from a GPS

5 Figure 1. Snapshot of (a) TEC (in TECU) and (b) meridional wind over the North American continent obtained from our Full Physics-Based data assimilation model and the corresponding values from our ionospheric model (c) without data assimilation and (d) from HWM. receiver located nearby at Goddard Space Flight Center (38 N, 75 W) (black line), and from the data assimilation model (red line) and from the ionosphereplasmasphere model without data assimilation (blue line). Note that a significant day-to-day variability of about 30% was observed in TEC over this station during this period. Also note that the data assimilation model captures the observed day-to-day variability very well, whereas the model without data assimilation, as expected, does not follow the day-to-day changes. The good agreement between the data assimilation model TEC values and the GPS data is, however, expected since the data from this station had been assimilated in the model run. The time series of the meridional neutral wind at 300 km altitude, as obtained from our data assimilation model (red and black lines) and from the HWM model (blue line), is shown in Figure 2 (bottom) for these 4 days. Although the obtained wind pattern follows the general HWM morphology with poleward winds during the day and equatorward winds during the night, significant differences can be seen in the morning reversal times and in the daytime amplitudes Low-Latitude Kalman Filter Example [17] In the second example, we have used our Full Physics-Based Kalman filter model to study the morphology of the low-latitude ionosphere. Recently, Immel et al. [2006] have presented a 30-day averaged IMAGE FUV images of the nm recombination airglow between 2030 and 2200 LT that clearly show a four-cell longitude pattern in the brightness of the equatorial anomalies. They attributed this pattern to daytime, E region dynamo winds associated with the nonmigrating, eastward propagating wave number 3 diurnal tide (DE3) [Hagan and Forbes, 2002]. Scherliess et al. [2008] have used 13 years of TOPEX TEC observations to establish the seasonal, solar cycle, local time, and geomagnetic activity dependence of this pattern. In the following 5of8

6 Figure 2. Temporal variation of (top) TEC and of (bottom) the meridional neutral wind over Wallops Island for our 4-day period. example, we have assimilated COSMIC radio occultation data in our Full Physics-Based Data assimilation model in order to investigate if these low-latitude patterns can also be observed in the data assimilation results. [18] For this study, the radio occultation data from the six COSMIC satellites were continuously assimilated over a 4-day period in April 2007 (days 90 93) and the model, in return, provided the 3-D electron density distribution from 90 km to geosynchronous altitude (30,000 km). Figure 3 shows, as an example, a TEC map obtained from our model results for 1 April of8 The results pertain to a fixed solar local time (SLT = 1730) and are shown as a function of geographic longitude and latitude. The vertical TEC data were obtained by integrating through the 3-D ionosphereplasmasphere from 90 km to the upper boundary. The four TEC peaks seen in Figure 3 are collocated with the four peaks observed in the TOPEX TEC data for this local time and season [Scherliess et al., 2008] and are believed to be associated with the wave number three tidal forcing (DE3). An inspection of the three-dimensional model densities (not shown here) indicates that the observed wave number four signatures are also evident

7 Figure 3. Example of a TEC map obtained from our Full Physics-Based Kalman filter model for 1 April The TEC values are given in TECU and shown for a fixed solar local time (SLT is 1730). Clearly seen is the wave number four structure in the low-latitude TEC distribution. in the equatorial and low-latitude F region peak heights (hmf2) and peak densities (NmF2). In future studies, we will use the model in order to investigate the day-today variability of these density structures. 4. Summary and Conclusions [19] We have developed a new physics-based Kalman filter data assimilation model for the ionosphere that is based on a physics-based model of the ionosphereplasmasphere system and an ensemble Kalman filter technique. The model covers the ionosphere-plasmasphere from 90 km to nearly geosynchronous altitudes and can assimilate a variety of different data types, including GPS/TEC from hundreds of ground-based receivers, in situ N e from several DMSP satellites, bottomside N e profiles from tens of ionosondes, and occultation data from the six COSMIC satellites. One of the main strengths of this model is that in addition to its specification of the plasma densities it also provides specification for the corresponding ionospheric driving forces, including the equatorial and low-latitude electric fields, and the neutral wind and composition. Here we have used the model to study the morphology and dynamics of the low-latitude and midlatitude ionosphere during two 4-day long periods in March 2004 and April Our results indicate that the model can reliably specify the ionospheric plasma densities at low latitudes and midlatitudes. In particular, we found that the model was able to specify the low-latitude four-cell longitude pattern that had recently been observed in TEC and UV observations. At midlatitudes, we found that the meridional neutral wind obtained from our data assimilation model follows the general morphology of the HWM wind. However, our model results significantly differ from HWM in the morning reversal times and in the daytime wind amplitudes. These changes in the wind pattern can account for the observed 30% day-to-day variability seen in TEC at Wallops Island during our study period. In future studies, we will use our new model to further investigate the morphology and variability of the low-latitude and midlatitude ionosphere and its corresponding drivers. [20] Acknowledgment. This research was supported by ONR grant N to Utah State University. References Angling, M. J., and B. Khattatov (2006), Comparative study of two assimilative models of the ionosphere, Radio Sci., 41, RS5S20, doi: /2005rs Coster, A. J., J. C. Foster, and P. J. Erickson (2003), Monitoring the ionosphere with GPS, GPS World, Daley, R. (1991), Atmospheric Data Analysis, Cambridge Univ. Press, Cambridge, U. K. 7of8

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Schunk (2006), The Utah State University Gauss-Markov Kalman filter of the ionosphere: The effects of slant TEC and electron density profile data on model fidelity, J. Atmos. Sol. Terr. Phys., doi: /j.jastp Thompson, D. C., L. Scherliess, J. J. Sojka, and R. W. Schunk (2009), Plasmasphere and upper ionosphere contributions and corrections during the assimilation of GPS slant TEC, Radio Sci., 44, RS0A02, doi: /2008rs L. Scherliess, R. W. Schunk, and D. C. Thompson, Center for Atmospheric and Space Sciences, Utah State University, Logan, UT 84322, USA. (ludger@gaim.cass.usu.edu) 8of8