Application of data assimilation in the Whole Atmosphere Community Climate Model to the study of day-to-day variability in the middle and upper atmosphere


Corresponding author: N. M. Pedatella, High Altitude Observatory, National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307-3000, USA. (


[1] The Data Assimilation Research Testbed (DART) ensemble adjustment Kalman filter (EAKF) is employed to perform data assimilation in the Whole Atmosphere Community Climate Model (WACCM). To demonstrate the potential of the WACCM+DART for studying short-term variability in the mesosphere and lower thermosphere (MLT), results are presented based on the assimilation of synthetic observations that are sampled from a known model truth. We assimilate temperature and wind from radiosondes and aircraft, satellite drift winds, and COSMIC refractivity in the lower atmosphere, and SABER temperature observations in the middle/upper atmosphere. Relative to an unconstrained WACCM simulation, the assimilation of only lower atmosphere observations reduces the global root mean square error (RMSE) in zonal wind by up to 40% at MLT altitudes. Using data assimilation to constrain the lower atmosphere can therefore provide significant insight into MLT variability. The RMSE in the MLT is reduced by an additional 10–15% when SABER observations are also assimilated. The WACCM+DART is shown to be able to reproduce the large-scale features of the day-to-day variability in the zonal mean, migrating, and nonmigrating tides in the MLT. Though our simulation results are based on idealized conditions, they demonstrate that the WACCM+DART can reproduce the day-to-day variability in the MLT. Assimilation of real observations in the WACCM+DART will therefore enable significant insight into the real day-to-day dynamical variability from the surface to the lower thermosphere.

1 Introduction

[2] A prominent feature of the mesosphere and lower thermosphere (MLT) is the presence of large amplitude diurnal and semidiurnal atmospheric tidal oscillations. The tides in the MLT are comprised of both migrating and nonmigrating tides. Migrating tides propagate westward with a zonal phase speed equal to the apparent motion of the Sun, while nonmigrating tides may propagate either eastward or westward and have a zonal phase speed that is either faster or slower than the apparent solar motion. Though they originate in the troposphere and stratosphere, the tidal amplitude increases exponentially with height, resulting in the largest amplitudes occurring in the MLT where tidal growth is halted due to dissipative processes. Given their large amplitudes, MLT tidal variability is of utmost importance for understanding the global-scale dynamics in the MLT. The study of tidal variability on daily, seasonal, and interannual timescales has therefore attracted significant attention [e.g., Vincent et al., 1999; She et al., 2004; Oberheide et al., 2009]. Recent satellite observations have significantly improved the understanding of tidal variability on seasonal and interannual timescales [Forbes et al., 2008; Oberheide et al., 2009]; however, thorough knowledge of the short-term, day-to-day, tidal variability remains deficient due to insufficient temporal resolution of current global satellite observations. The study of day-to-day tidal variability in the MLT is therefore largely confined to ground-based observations, which do not provide information regarding the global structure of the tidal oscillation [Harris and Vincent, 1993; She et al., 2004]. The lack of global information prevents determining if the source of observed tidal variability is primarily due to changes in the migrating or nonmigrating solar tides, and ground-based observations thus only provide limited information on the tidal variability.

[3] Under the correct constraints, global numerical models can provide significant insight into the observed day-to-day dynamical variability in the MLT. The primary advantage of using global models in the study of day-to-day variability is that they can be used to place sparse ground-based observations within a global context, allowing for a determination of how variability in different migrating and nonmigrating tides combine to produce the observed variability at a single location [Liu et al., 2007]. Though free-running (i.e., unconstrained) simulations reveal significant day-to-day tidal variability [Liu, 2013], the utility of global models for studying the real dynamical variability in the MLT is dependent upon adequately constraining the model, especially in the lower atmosphere [Liu et al., 2009]. This can be done through application of the appropriate boundary conditions [Liu et al., 2007], nudging the model toward reanalysis fields [Jin et al., 2012], or through data assimilation [Wang et al., 2011].

[4] Motivated by the need for adequate representation of the day-to-day dynamical variability of the MLT on global scales, the data assimilation capability has recently been added to the Whole Atmosphere Community Climate Model (WACCM). The data assimilation is implemented using the ensemble adjustment Kalman filter (EAKF) [Anderson, 2001] provided by the Data Assimilation and Research Testbed (DART). Data assimilation in whole atmosphere models has previously been performed using the three-dimensional variational (3D-Var) technique [Hoppel et al., 2008; Polavarapu et al., 2005; Wang et al., 2011], and the present work adopts the EAKF approach, which offers potentially significant advantages for performing data assimilation in a whole atmosphere model. In particular, the use of the EAKF eliminates the need to specify the background error covariances that are required in the 3D-Var technique. Determining the covariances in whole atmosphere models is dependent upon the method used, and may introduce spurious correlations [e.g., Polavarapu et al., 2005]. In contrast, the EAKF relies on the ensemble of model simulations to determine the covariances. This should result in an improved representation of the covariance, leading to improvements in the data assimilation. In the present study, we detail the implementation of the DART EAKF in WACCM, and present initial results to demonstrate the capability of the WACCM+DART assimilation system for studying day-to-day variability in the MLT. We additionally discuss the importance of the lower atmosphere for generating variability in the MLT, as well as the impact of middle/upper atmosphere observations on the assimilation results.


[5] WACCM is the vertical extension of the National Center for Atmospheric Research (NCAR) Community Atmosphere Model (CAM) from 2 hPa (∼45 km) up to 5×10−6 hPa (∼145 km). In addition to the lower atmosphere chemical, dynamical, and physical processes in CAM, WACCM includes the necessary additional processes that are required to model the upper stratosphere, mesosphere, and lower thermosphere. In the present study, we use WACCM4, which is part of the Community Earth System Model (CESM) version 1.1.1 ( The model is run at a horizontal resolution of 1.9°×2.5° in latitude and longitude, and includes 66 vertical levels. We refer the reader to Garcia et al. [2007], Marsh et al. [2007], and Richter et al. [2010] for a thorough discussion of WACCM.

[6] The data assimilation is incorporated into WACCM using the DART EAKF. DART is an open-source, community, software package that provides a framework, which is independent of the model, for performing ensemble data assimilation. DART can therefore be applied to models with a wide range of complexity [Anderson et al., 2009] ( Raeder et al. [2012] have previously used DART to perform data assimilation in CAM. Since CAM and WACCM are both part of the CESM framework, the WACCM+DART data assimilation system generally follows the methodology of Raeder et al. [2012]. However, some changes were required due to the increased vertical domain of WACCM compared to CAM. The most notable change is that we specify the vertical localization using a Gaspari-Cohn function [Gaspari and Cohn, 1999] with a half width of 0.5 in ln(p/p0) coordinates, where p is pressure and p0 is the surface pressure. This differs from the vertical localization of 1000 hPa in pused by Raeder et al. [2012]. Our vertical localization corresponds to a half width of ∼0.5 scale height, and this value was selected due to its performance relative to other vertical localizations that were tested. A Gaspari-Cohn function with a half width of 0.2 radians is used for the horizontal localization. An additional change was necessary to prevent the occurrence of instabilities due to large amplitude perturbations near the model upper boundary. Large adjustments introduced by the data assimilation at lower model levels were found to introduce spurious waves that grew to unrealistically large amplitudes at the model upper boundary. To prevent model instabilities at the model upper boundary, we have doubled the second-order divergence damping coefficient in WACCM. This change does not significantly influence WACCM results in the MLT.

[7] To illustrate the capabilities of WACCM+DART for studying the day-to-day variability in the middle and upper atmosphere, we have performed an Observation Simulation System Experiment (OSSE). The OSSE uses synthetic observations that are generated by sampling a WACCM simulation at the location of real observations from 5–25 November 2008. Realistic observational errors are specified for the synthetic observations. Similar to Raeder et al. [2012], the lower atmosphere observations include all observations used in the NCEP-NCAR reanalysis (temperature and wind from radiosondes, aircraft, and satellite drift winds) and COSMIC radio occultation observations. Note that satellite radiances are not assimilated in the present study. We additionally assimilate SABER temperature observations between 20 and 100 km to provide an observational constraint for altitudes that are above the conventional lower atmosphere observations. Although the lower atmosphere is densely sampled, it should be noted that SABER only provides relatively sparse observations of the middle/upper atmosphere. The SABER observations are quasi sun synchronous, and this results in only having observations at a few (typically four) longitude sectors at each assimilation time. For the time period considered, SABER observed near 1300 and 2200 local time, and between 50°S and 80°N. It is important to consider the performance of WACCM+DART in the MLT in the context of the relatively sparse middle/upper atmosphere observations that are assimilated. The assimilation is performed every 6 h; however, to prevent damping of the tides, we only assimilate SABER observations that are within ±1.5 h of the assimilation time. The quality of the assimilation is expected to improve by using forward operators that use multiple forecast model times to accurately interpolate prior estimates of observations to the exact time of the observations. In particular, this may improve results in the MLT by permitting the use of additional observations without the possibility of damping tidal oscillations. This could also be accomplished by performing the assimilation at a higher frequency. To prevent collapse of the model spread, prior to the assimilation, the ensemble is inflated using the spatially and temporally varying inflation approach of Anderson [2009]. In the following, we present results from three different 40 member ensemble simulations. Each simulation was initialized with the same ensemble, and the simulations differ only in the data used in the assimilation. The initial conditions for each ensemble member were obtained from the model state at 0UT on 1–10 November from four different free running WACCM simulations. The simulations either assimilated no observations (control), assimilated only lower atmosphere (LA) observations, or assimilated lower atmosphere and SABER (LA+S) observations. The control simulation reflects the climatological variability of WACCM. When assimilating only lower atmosphere observations, the observations only influence the model state up to ∼2 hPa, and the model is not directly constrained at higher altitudes.

3 Results

[8] The zonal mean zonal wind results at 1×10−4 hPa (∼110 km) for the simulation truth, LA, and LA+S simulations are shown in Figures 1a–1c. The results shown are the ensemble mean of the 6 h forecast state (i.e., the state prior to performing the assimilation at a given time). Note that we limit our attention to 15–25 November. This is after any initial adjustment period, and the results presented are thus representative of the assimilation performance under quasi-steady state conditions. In general, the large-scale latitude and day-to-day variability present in the simulation truth is captured by both the LA and LA+S simulations. This is evident in the ability of the assimilation to capture the enhanced eastward winds in the Southern Hemisphere and greater westward winds near 20°N that occur between 17 and 20 November. There are, however, several aspects of the simulation truth that are not reproduced in the LA and LA+S simulations. In particular, much of the smaller scale variability in the truth simulation is absent in the LA and LA+S simulations. As an example, the short-lived enhancements that occur near 30°S on 19 and 24 November in the simulation truth are significantly weaker in the LA and LA+S simulations. This suggests that, although the SABER observations improve the assimilation results, the SABER observations alone are unable to fully constrain the model state in the MLT.

Figure 1.

Zonal mean zonal wind at 1×10−4 hPa for the (a) simulation truth, (b) LA, and (c) LA+S simulations. (d) Global RMSE for the control (black), LA (blue), and LA+S (red) simulations at 516 hPa (dashed) and 1×10−4 hPa (solid).

[9] The global average root mean square error (RMSE) for the zonal mean zonal wind at 516 hPa and 1×10−4 hPa are shown in Figure 1d. The RMSE at 516 hPa is shown in Figure 1d to briefly illustrate the performance of WACCM+DART in the troposphere. In the absence of any observational constraint, the global average RMSE at 516 hPa is 8–10 m s−1. The data assimilation reduces the global average RMSE by ∼70% to roughly 2.5 m s−1for both the LA and LA+S simulations. The significant reduction of the RMSE at 516 hPa illustrates the effectiveness of WACCM+DART at tropospheric altitudes. As the present study is focused on the MLT, we do not present extensive validation of the tropospheric results; however, we have verified that the performance of WACCM+DART is comparable to the Raeder et al. [2012] CAM+DART results in the troposphere. The WACCM+DART data assimilation is also able to significantly reduce the RMSE in the MLT. The RMSE for the control simulation is 40–45 m s−1, and this is reduced to around 30 m s−1and 25 m s−1 for the LA and LA+S simulations, respectively. Data assimilation in the lower atmosphere is therefore able to reduce the error in the MLT by ∼30%, and this illustrates the correlation between variability in the lower atmosphere and the MLT. Assimilation of the SABER observations can further reduce the RMSE by an additional 15–20%. Therefore, in addition to lower atmosphere observations, observations in the middle/upper atmosphere are also important to include in the assimilation in order to accurately specify the dynamics of the MLT. Compared to the troposphere, the RMSE is significantly larger in the MLT. However, the greater error in the MLT needs to be considered in the context of the relatively sparse SABER observations that are assimilated, and we believe that the RMSE at MLT altitudes would improve significantly with comprehensive observations of the middle/upper atmosphere. The larger RMSE at MLT altitudes may also be related to the greater dynamical variability at these altitudes which is illustrated by the larger RMSE in the control simulation. The combination of greater dynamical variability and sparse observations may limit the current capability of the data assimilation at MLT altitudes. The results in Figure 1 do, however, demonstrate that the WACCM+DART is able to reproduce the larger scale day-to-day variability in the zonal mean zonal wind from the surface to the lower thermosphere.

[10] The ensemble average of the nonmigrating eastward propagating diurnal tide with zonal wave number 3 (DE3) and the semidiurnal migrating tide (SW2) in temperature at 115 km are presented in Figure 2. Understanding the variability in the DE3 and SW2 is important due to their influence on the MLT dynamics as well as their influence on day-to-day ionosphere variability [England, 2012; Liu and Richmond, 2013]. We have thus chosen to focus on these tides for the purpose of demonstrating the ability of the WACCM+DART to reproduce the day-to-day tidal variability. Figures 2a and 2d reveal that significant day-to-day amplitude variability occurs in the simulated truth for the DE3 and SW2. The ability of the LA and LA+S simulations to capture the DE3 and SW2 variability is similar to the previously discussed assimilation results for the zonal mean zonal wind in the MLT. The WACCM+DART assimilation is again able to reproduce the large scale day-to-day tidal variability, but is not able to reproduce the smaller scale variability. The LA simulation again reproduces much of the day-to-day tidal variability, and this provides additional evidence for the correlation between lower atmosphere variability and variability in the middle/upper atmosphere. The LA simulation reduces the latitude average RMSE at 115 km by ∼15% and ∼20% compared to the control simulation for the DE3 and SW2, respectively. Assimilating SABER observations reduces the RMSE by an additional 15% for the DE3 and 10% for the SW2. This provides additional evidence that including middle/upper atmosphere observations in WACCM+DART is important for accurate modeling of MLT altitudes.

Figure 2.

The DE3 in temperature at 115 km for the (a) simulation truth, (b) LA, and (c) LA+S simulations. (e–g) Same as in Figures 2a–2c except for the SW2.

[11] The previous results have focused on global-scale dynamical features of the MLT, and we now briefly discuss the performance of WACCM+DART at a single location. Results for the zonal wind at 31°N and 255°E and between 60 and 125 km are shown in Figure 3. The results in Figure 3 can be thought of as representative of what may be seen from a single ground-based observation. The simulation truth (Figure 3a) contains rich spectra of spatial and temporal variability. Considering the scales of the variability, the LA and LA+S simulations perform remarkably well in terms of reproducing the true variability. In particular, the strong tidal oscillations that occur around 100–120 km are well reproduced in both the LA and LA+S simulations. Similar to the previous results, the primary deficiency is the ability of the assimilation to capture all of the smaller scale variability. The RMSE averaged between 60 and 120 km for the control, LA, and LA+S simulations is shown in Figure 3d. The results in Figure 3d again illustrate that the assimilation of only lower atmosphere observations can significantly reduce the RMSE at MLT altitudes, and that inclusion of the SABER observations further improves the assimilation results. The results in Figure 3 demonstrate that WACCM+DART can adequately reproduce the dynamical variability that would be observed from a single ground-based observatory. WACCM+DART can thus provide a useful tool for placing observed variability at a single location within the context of the global-scale dynamical variability.

Figure 3.

The zonal wind at 31°N, 255°E for the (a) simulation truth, (b) LA, and (c) LA+S simulations.(d) The RMSE between 60 and 120 km for the control (black), LA (blue), and LA+S (red) simulations.

4 Conclusions

[12] In the present study we have presented results illustrating the use of the DART EAKF to perform ensemble data assimilation in WACCM. The results demonstrate that WACCM+DART is capable of reproducing the large-scale features of the day-to-day variability in the zonal mean, migrating, and nonmigrating tides in the MLT. In addition to the global-scale dynamics, WACCM+DART captures the dynamical variability at a single location, such as would be observed from an individual ground-based observation. Compared to unconstrained WACCM simulations, the assimilation of lower atmosphere observations alone can reduce the zonal wind RMSE in the MLT by 30–40%, and inclusion of middle/upper atmosphere temperature observations from SABER reduces the zonal wind error by an additional 10–15%. Sufficient constraint of the lower atmosphere through data assimilation can therefore provide considerable insight into the variability at MLT altitudes. Nonetheless, even relatively sparse middle/upper atmosphere observations have a significant impact, and assimilating the limited available middle/upper atmosphere observations is therefore of immense value for determining the day-to-day dynamical variability in the MLT.

[13] As demonstrated by the results, WACCM+DART can be used to improve understanding of the short-term variability throughout the middle and upper atmosphere. Though the present study has focused on synthetic observations obtained from a known model truth, we have also assimilated real observations, and results pertaining to the assimilation of real observations will be presented in a forthcoming paper. By assimilating real observations, WACCM+DART can be used to understand, and potentially predict, the global-scale day-to-day variability from the surface to the lower thermosphere. Dynamical variability at these altitudes is an important source of day-to-day variability in the ionosphere and thermosphere, and WACCM+DART can thus lead to improved understanding of the ionosphere-thermosphere variability that is driven by the lower atmosphere.


[14] The National Center for Atmospheric Research is sponsored by the National Science Foundation. This work was supported in part by a NCAR Advanced Study Program Postdoctoral Fellowship (N. Pedatella), and from NSF grant AGS-1138784 and NASA LWS grant NNX09AJ83G.

[15] The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.