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Assessing the performance of thermospheric modelling with data assimilation throughout solar cycles 23 and 24.
Office, Exeter, Devon, UK. Toulouse, France.
Copyright 2015 by the American Geophysical Union.
MURRAY ET AL.: THERMOSPHERIC MODELLING DURING SOLAR CYCLES 23 AND 24.
50% in the case that as many as nine ensemble members are used. Codrescu et al.  found the error of their model initial state reduced from ∼25% to ∼10% using an EnKF technique with ten members. Matsuo et al.  used EnKF with inferred neutral density satellite observations to improve a model neutral density specification in the vicinity of the satellite. Matsuo et al. found that a global impact was achieved if accompanied by the estimation of the primary driver of the density variable (such as solar EUV flux), highlighting the importance of external forcing to the system. Two data assimilation methods were developed in ATMOP; one using DTM-2012, and the other TIEGCM. A version of DTM was developed that can assimilate total density data in near-real time, which will make orbit predictions significantly more accurate. Data assimilation techniques were also developed for use with TIEGCM with the aim to create a more physically accurate global analysis and forecast system for the thermosphere. While the assimilation methods developed are described in detail elsewhere [see Bruinsma et al., 2012, and Henley et al, manuscript in preparation], this paper provides first results of an intercomparison of the newly developed models. Both TIEGCM and DTM-2012 are compared with observations taken at various periods throughout solar cycles 23 and 24 in order to determine if a more complex physical model with data assimilation could be more accurate for forecasting efforts than the currentlyused empirical methods. This validation effort is crucial to determine if these new techniques are beneficial for current space weather operations. The observations and models used for the comparison will be outlined in Section 2, and methods used for analysis described in Section 3. The results of the study will be presented in Section 4, while some conclusions of the findings and possible future work will be discussed in Section 5.
mean and 1-day delayed solar radio flux at 10.7cm (F10.7) are used as solar inputs, and the Am geomagnetic index is also used. DTM is constructed by fitting to the underlying density database, as good as possible in the least-squares sense, to reproduce the mean climatology of the thermosphere [see Bruinsma et al., 2004]. The result includes a density value at a particular latitude and longitude between 200–1000 km, with up to 1◦ resolution. Errors on short time scales of a few days or less can be of the order of tens of percent. A more detailed description of the updated DTM with data assimilation can be found in Bruinsma et al. . The physical model used in this work, TIEGCM, is a firstprinciples, three-dimensional, non-linear representation of the coupled thermosphere and ionosphere system. TIEGCM uses spherical geographic coordinates, with latitude ranging from −87.5◦ to 87.5◦ in 5◦ increments, longitude ranging from −180◦ to 180◦ in 5◦ increments, and a 60-second time step. The lower boundary at ∼97 km extends up to ∼500– 700 km depending on solar activity. The migrating and semi-diurnal tides are specified at the lower boundary using the Global Scale Wave Model [Hagan et al., 1995], which does not consider the effects of planetary waves and nonmigrating tides. The vertical coordinate is a log-pressure scale, ln(p0 /p), where p is pressure and p0 is a reference pressure, and pressure levels range from −7 to 7 increasing in half-scale-height increments. Neutral density observations were assimilated into the model using an ensemble optimal interpolation method [EnOI; Oke et al., 2002; Evensen, 2003]. EnOI uses an ensemble approach to help determine how much trust to put in the model prediction at any given time (as opposed to how much trust to put in the observations). An ensemble of nine models are run offline, with each model regularly perturbed with smoothed random temperature fluctuations. A background density error covariance matrix is then calculated from these non-assimilative, independent ensemble members. This is combined with the background and observations to produce a density analysis. The analysis is then converted to a temperature analysis (as density is a derived field in TIEGCM), which is used to initialise the model run. This is the first time an EnOI method has been used for thermospheric data assimilation, with much previous work focusing on EnKF (see Section 1). For further details on the assimilation scheme, see Henley et al. (manuscript in preparation, 2015). For consistency with DTM input parameters, TIEGCM was run using the Heelis high-latitude ion convection model [Heelis et al., 1982] as a magnetospheric input, which uses F10.7 solar flux and Kp planetary geomagnetic index as inputs. The model provides various advantages for development, speed, robustness, and scientific return compared to empirical modelling. Results from TIEGCM have been previously compared favourably with CHAMP data on a large scale [Sutton, 2008; Qian and Solomon, 2012], although it has also been noted that TIEGCM RMS errors typically gradually increase with a decline in solar activity [Kim, 2011].
in preparation, 2015). In order to accurately compare the output of the two models, DTM was run for the particular altitude, latitude, and longitude of the spacecraft at time of observation. DTM densities were calculated every 5 or 10 seconds (depending whether CHAMP or GRACE was being compared), while TIEGCM resulting densities were saved every 15 minutes. It is worth noting that both CHAMP and GRACE spacecraft have different local times for the periods studied here, the difference ranging between ∼1–2 LT. It useful to compare the model results to these observations for validation purposes since they have an altitude difference of ∼100–150km for the time periods studied. However, a more in-depth comparison of latitudinal or longitudinal variation is not undertaken here. Typical model outputs are presented in Figure 1. A 2D map of DTM density at 2009 March 01 00:00UT is shown in the upper row, with an equivalent TIEGCM map in the middle row. CHAMP densities are also plotted in the lower row for an entire 90-minute orbit. Note the CHAMP spacecraft was at an altitude of ∼328km during this orbit, however the DTM and CHAMP densities have been interpolated to TIEGCM pressure level 21 (1.18 × 10−6 Pa) for ease of comparison. TIEGCM tends to have a narrower range of density values compared to DTM. It is also worth noting that both models overestimate the density in the points corresponding to the CHAMP measurements. This is a result that is emulated throughout solar minimum, as will be discussed in the following section.
tude. There is a clear difference during solar maximum, with TIEGCM being more accurate at these times, and both models underestimating the CHAMP density associated with higher activity. The sharp changes in density during the Hallowe’en storms result in values being smaller during this period, however TIEGCM again outperforms DTM here, most significantly when compared with the GRACE observations (as is clear from Figure 4, DTM overestimates the density values at the peaks).
Figure 5. Left column: CHAMP, DTM, and TIEGCM densities over 12 hours. Right column: Density difference between CHAMP observations and the two models. The upper to lower rows show results for 12 hours on 2009 March 15, 2003 March 15, and 2003 October 15, respectively. The altitude of the CHAMP spacecraft during these periods varied between ∼346–317 km, ∼432–401 km, and ∼422–391 km. The table also notes the differences between running TIEGCM with and without data assimilation, as it is worth determining how much of an improvement the assimilation system made to the physical model. Similar comparisons for DTM are presented in Bruinsma et al. . The results indicate that using the EnOI data assimilation technique has a small positive impact on the TIEGCM results, improving performance by ∼4% overall when a 1-hour assimilation cycle is used. The data assimilation technique improves the results greater during periods of solar maximum than minimum, the largest improvement found during the Hallowe’en storms.
5. Discussion and Conclusions This paper has characterised the relative merit of two new modelling approaches with data assimilation capabilities developed during the ATMOP project; the physical model, TIEGCM, and the semi-empirical model, DTM. This has been done for 60-day periods for equinox at solar minimum (from 2009 March), solar maximum (from 2003 March), and the Hallowe’en 2003 storms (from 2003 October). Model results were validated against satellite data to investigate whether the improved physical model can outperform the semi-empirical model that is currently used operationally.
height did not have a major impact, with similar errors found to previous results. However, with such limited observations used during assimilation (one data point rather than a whole 2D map at each timestep) this is likely highlighting the accuracy of the model rather than saying too much about the assimilation procedure. As mentioned previously, the satellites are at slightly different local times, and enhanced He concentrations are found at the higher GRACE altitude particularly during the deep solar minimum in 2009. This likely introduces additional density errors that may counteract the positive impact of assimilating CHAMP data at these altitudes. At the lower altitudes, a positive but limited improvement has been obtained using data assimilation with a general circulation model, with an overall improvement of ∼4% found. Including more relevant observations in the assimilation procedure would likely increase this percentage improvement. Future work will also include improvements to the data assimilation techniques developed in the ATMOP project, particularly implementing incremental analysis updates (see Henley et al., manuscript in preparation, 2015, for further discussion). The EnOI method developed could be converted to an EnKF system without much difficulty. An EnOI system is similar to EnKF, however information from the observations which improve the main model does not feed back into the ensemble. Assessment of the other versions of DTM also developed as part of the ATMOP project could be undertaken using the same method as in this paper. DTM2013 is supplemented by 2.5 years of GOCE satellite data, uses the 30 cm radio flux as a solar proxy, and 3-hour Am index as geomagnetic proxy. To improve predictions to 3-days out, another method (DTM-nrt) was developed to predict temperature corrections to DTM based on a neural network. Recent research highlights that the DTM-nrt version of the model is more accurate than the DTM-2012 studied here for 24-hour forecasts [Choury et al., 2013]. Comparisons to and assimilation of other types of observations would also be beneficial, for example Fabry-Per´ ot interferometer wind measurements, or total electron content. An increase in the availability of more real-time in-situ observations of the thermosphere will aid this work and space weather forecasting in general. Data from missions such as SWARM [Friis-Christensen et al., 2006] and Drag and Atmospheric Neutral Density Explorer [Pilinski , 2008] may prove useful for this purpose. With further improvements, the use of general circulation models in operational forecasting, in addition to empirical models currently used, is certainly plausible. Future work will allow near-real-time assimilation of thermospheric data into TIEGCM for forecasting. Acknowledgments. This work was supported by the European Framework Package 7 Advanced Thermosphere Modelling for Orbit Prediction project (Work Package 5.6). Data from CHAMP and GRACE missions are made available to the community by the Information Systems and Data Center at GFZ (http://isdc.gfz-potsdam.de). Model code for TIEGCM and DTM are made freely available to the community by NCAR (http://www.hao.ucar.edu/modeling/tgcm/) and the ATMOP project (http://www.atmop.eu) respectively. The authors thank the anonymous referees for their constructive suggestions to improve the manuscript. c British Crown Copyright 2015, the Met Office.
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