A data assimilation system with a four-dimensional local ensemble transform Kalman filter (4D-LETKF) is developed to make a new analysis dataset for the atmosphere up to the lower thermosphere using the Japanese Atmospherics General Circulation model for Upper Atmosphere Research. The time period from 10 January to 20 February 2017, when an international radar network observation campaign was performed, is focused on. The model resolution is T42L124, which can resolve phenomena at synoptic and larger scales. A conventional observation dataset provided by the National Centers for Environmental Prediction, PREPBUFR, and satellite temperature data from the Aura Microwave Limb Sounder (MLS) for the stratosphere and mesosphere are assimilated. First, the performance of the forecast model is improved by modifying the vertical profile of the horizontal diffusion coefficient and modifying the source intensity in the non-orographic gravity wave parameterization by comparing it with radar wind observations in the mesosphere. Second, the MLS observational bias is estimated as a function of the month and latitude and removed before the data assimilation. Third, data assimilation parameters, such as the degree of gross error check, localization length, inflation factor, and assimilation window, are optimized based on a series of sensitivity tests. The effect of increasing the ensemble member size is also examined. The obtained global data are evaluated by comparison with the Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA-2) reanalysis data covering pressure levels up to 0.1 hPa and by the radar mesospheric observations, which are not assimilated.
It is well known that the earth's climate is remotely coupled: for example, when El Niño occurs, convective activity in the tropics strongly affects midlatitude climate with the appearance of the Pacific–North American pattern (Horel and Wallace, 1981). Convective activity in maritime continents also modulates midlatitude climates by generating the Pacific–Japan pattern (Nitta, 1987). Most of these climate couplings between the tropics and midlatitude regions are caused by the horizontal propagation of stationary Rossby waves (Holton and Hakim, 2013). Teleconnection through stratospheric processes has also been known. For example, the sea-level pressure in the Arctic rises during El Niño. It was shown that this teleconnection occurs by modulation of planetary wave intensity and propagation in the stratosphere (Cagnazzo and Manzini, 2009). It is also well known that the occurrence frequency of stratospheric sudden warming (SSW), which exerts a strong influence on the Arctic oscillation of sea-level pressure (Baldwin and Dunkerton, 2001), is high during the easterly phase of the quasi-biennial oscillation (QBO) in the equatorial stratosphere (Holton and Tan, 1980). This is also due to the modulation of the propagation of planetary waves in the stratosphere. Thus, the stratosphere is an important area that brings about the remote coupling of climate.
Recently, the presence of interhemispheric coupling through the mesosphere has been reported as well. When the temperature in the polar winter stratosphere is high, the temperature in the polar summer upper mesosphere is also high, with a slight delay (Karlsson et al., 2009). This coupling is clear for at least a 1-month average (Gumbel and Karlsson, 2011). The interhemispheric coupling, which is initiated by SSW in the winter hemisphere, occurs at shorter timescales (Körnich and Becker, 2010). When SSW occurs in association with the breaking of strong planetary waves originating from the troposphere, the westerly wind of the polar night jet significantly weakens or, in strong cases, even turns easterly. The critical-level filtering of the gravity waves toward the mesosphere is then modulated, and the gravity wave forcing that drives the mesospheric meridional circulation with an upward (downward) branch on the equatorial (polar) side becomes weak. Thus, the temperature in the equatorial region increases and the poleward temperature gradient in the summer hemisphere weakens. The weak wind layer above the easterly jet in the summer hemisphere lowers so as to satisfy the thermal wind relation. The eastward gravity wave forcing region near the weak wind layer also descends and the upward branch of the meridional circulation, which maintains extremely low temperature in the summer polar upper mesosphere, weakens.
However, there is little observational evidence of gravity wave modulation in
the mesosphere. The Interhemispheric Coupling Study by Observations and
Modeling (ICSOM:
In the ICSOM project, we are also proceeding with a model study using a gravity-wave-permitting high-top general atmospheric circulation model (GCM) that covers the entire troposphere and middle atmosphere (up to the lower thermosphere) simultaneously. However, this is not easy because the GCMs including the entire middle atmosphere are not yet sufficiently mature even for relatively low resolutions that do not allow explicit gravity wave simulation (e.g., Smith et al., 2017). Therefore, verification of the GCMs by high-resolution observations is necessary. In the ICSOM project, by validating the high-top GCM using data from the comprehensive international radar observation campaigns, it is expected to reproduce high-resolution global data with high reliability. Using these global data, we plan to confirm the regional representation of gravity wave characteristics detected by each radar and deepen the understanding of interhemispheric coupling quantitatively with a resolution of gravity wave scales.
Gravity wave simulation research using high-resolution GCMs has been performed in the past (e.g., Hamilton et al., 1999; Sato et al., 1999, 2009, 2012; Watanabe et al., 2008; Holt et al., 2016). However, reproducing gravity wave fields in the global atmosphere at a specific date and time requires significant effort (Eckermann et al., 2018; Becker et al., 2004). Data assimilation up to the scale of gravity waves is ideal to create global high-resolution grid data sequentially. However, current data assimilation schemes work well for geostrophic motions such as Rossby waves but not necessarily for ageostrophic motions such as gravity waves. Recent studies (Jewtoukoff, et al., 2015; Ehard et al., 2018) reported that gravity waves observed in the European Center for Medium-Range Weather Forecasts (ECMWF) operational data are partly realistic in the lower and middle stratosphere, but more validation with observation data is necessary. It has also been shown that the difference in horizontal winds between reanalysis datasets is quite large in the equatorial region where the Coriolis parameter becomes zero (Kawatani et al., 2016). The reasons for this problem may be the insufficient maturity of the models to accurately express ageostrophic motions and/or the shortage of observation data, including gravity waves, to be assimilated.
Data assimilation for the mesosphere is particularly not easy, partly because the energy ratio of Rossby waves and gravity waves is reversed there (Shepherd et al., 2000) and partly because observational data for the mesosphere are significantly limited compared to those for the lower atmosphere. In addition, it has been shown that, in the upper stratosphere and the mesosphere, Rossby waves are generated in situ due to baroclinic–barotropic instability caused by wave forcing associated with breaking or critical-level absorption of gravity waves propagating from the troposphere (Watanabe et al., 2009; Ern et al., 2013; Sato and Nomoto, 2015; Sato et al., 2018). It has been found that gravity waves are spontaneously generated in the middle atmosphere from the imbalance of the polar night jet (Sato and Yoshiki, 2008; Snyder et al., 2007; Shibuya et al., 2017), from an imbalance caused by the wave forcing due to primary gravity waves (Vadas and Becker, 2018; Hayashi and Sato, 2018), and also by shear instability caused by primary gravity wave forcing (Yasui et al., 2018). The Rossby wave generation in the middle atmosphere due to primary gravity wave forcing is regarded as a compensation problem, which makes it difficult to understand the change in the Brewer–Dobson circulation in terms of the relative roles of Rossby waves and gravity waves for climate projection with the models (Cohen et al., 2013). However, these instabilities and the in situ generation of waves in the middle atmosphere could significantly affect the momentum and energy budget in the middle atmosphere and above (Sato et al., 2018; Becker, 2017). Hence, it is necessary to understand the roles of these waves as accurately as possible based on credible, high-resolution model simulations validated by high-resolution observations.
In view of the situation described above, the following method may be one of the best existing ways to create high-resolution data for the entire middle atmosphere including gravity waves to understand the teleconnection through the mesosphere. First, a data assimilation is performed using a high-top but relatively low-resolution model to create grid data for the real atmosphere from the ground to the lower thermosphere including only larger-scale phenomena such as Rossby waves. Second, the analysis data obtained by the assimilation are used as initial values for a free run of high-resolution GCMs to simulate gravity waves. Eckermann et al. (2018) and Becker and Vadas (2018) have performed pioneering studies on the effectiveness of such free runs.
Reanalysis data over a long time period are produced using modern data assimilation schemes and released by meteorological organizations for climate analysis. These include the following: the ECMWF interim reanalysis (ERA-Interim; Dee et al., 2011) and the fifth reanalysis (ERA5; Hersbach et al., 2018) produced by a four-dimensional (4D) variational assimilation scheme (Var); MERRA (Rienecker et al., 2011) and the following version 2 (MERRA-2; Gelaro et al., 2017) by the National Aeronautics and Space Administration (NASA) by a three-dimensional Var (3D-Var); the National Centers for Environmental Prediction (NCEP) Climate Forecast System Reanalysis (CFSR; Saha et al., 2010) and the Climate Forecast System version 2 (CFSv2; Saha et al., 2014); and the Japanese 55-year reanalysis (JRA-55; Kobayashi et al., 2015) by a 4D-Var. ERA-Interim and JRA-55 cover up to a pressure of 0.1 hPa, NCEP/CFSR and NCEP/CFSv2 up to 0.266 hPa, and MERRA, MERRA-2, and ERA5 up to 0.1 hPa. However, global data for the middle and upper mesosphere to the lower thermosphere are not created regularly. As stated above, considering the importance of ageostrophic motions in the mesosphere and lower thermosphere (MLT), the data assimilation used for such meteorological organizations may not work very well for the middle stratosphere and above (Polavarapu et al., 2005). Therefore, in recent years, significant efforts have been made to assimilate data using GCMs that include the MLT region. Currently, the data available for studying the MLT region come from the Aura Microwave Limb Sounder (Aura MLS; beginning in 2004), Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED) Sounding of the Atmosphere using Broadband Emission Radiometry (SABER; beginning in 2002), and the Defense Meteorological Satellite Program (DMSP) Special Sensor Microwave Imager/Sounder (SSMIS; Swadley et al., 2008).
Global data for the atmosphere including the MLT region are valuable from the
following viewpoints. First, they can improve prediction of the polar
stratosphere (e.g., Hoppel et al., 2008, 2013; Polavarapu et al., 2005). It
seems that anomalies in the MLT region start about 1 week earlier than
stratospheric anomalies such as SSWs, propagating down to the troposphere.
Thus, better understanding the MLT physics and chemistry has the potential
to improve long-range weather forecasts. Second, it is possible to
quantitatively understand the transport of minor species from the MLT region
(e.g., Hoppel et al., 2008; Polavarapu et al., 2005). For example,
high-energy particles originating from the upper atmosphere contribute to
the production of
The first attempt to create analysis data for the whole middle atmosphere
using data assimilation was made by a Canadian group. They employed 3D-Var
using the Canadian Middle Atmosphere Model (CMAM) with full interactive
chemistry and nonlocal thermodynamic equilibrium (non-LTE) radiation
(Polavarapu et al., 2005; Nezlin et al., 2009). The assimilation of the data
in the troposphere and stratosphere has been shown to improve the analysis
of large-scale phenomena (zonal wavenumber
Nowadays whole-atmosphere models covering the surface to the exosphere have been developed (Akmaev, 2011). Data assimilation and data nudging studies using a whole-atmosphere model were performed focusing on the SSW in 2009. These include studies using the whole-atmosphere data assimilation system (WDAS), which includes the whole-atmosphere model and a 3D-Var analysis system (Wang et al., 2011), the Ground-to-topside model of Atmosphere and Ionosphere for Aeronomy (GAIA) with a nudging method (Jin et al., 2012), and SD-WACCM (Chandran et al., 2013; Sassi et al., 2013). Outputs from a long-term run using GAIA, which was nudged to the reanalysis data up to the lower stratosphere, were used for a momentum budget analysis in the whole middle atmosphere, and the importance of the in situ generation of gravity waves and Rossby waves in the middle atmosphere was suggested (Sato et al., 2018; Yasui et al., 2018).
Although most 4D data assimilation studies described above used 4D-Var, the
method using an ensemble Kalman filter is also possible. The 4D-Var codes
need to be developed for each model. In contrast, the four-dimensional local
ensemble transform Kalman filter (4D-LETKF) developed by Miyoshi and Yamane (2007), which is a statistical assimilation method, is versatile and can
thus be implemented in any model relatively easily. This study develops an
assimilation system using the 4D-LETKF with a GCM with a top in the lower
thermosphere. As the first step of the ICSOM project, we used a
low-resolution version of the GCM and examined the best parameters of the
assimilation system for the middle atmosphere (i.e., the atmosphere up to
the turbopause,
We used the Japanese Atmospheric GCM for Upper Atmosphere Research (Watanabe
and Miyahara, 2009) as a forecast model, which we refer to as JAGUAR in
this paper. This model has a high model top of approximately 150 km and is
based on the T213L256 middle atmosphere GCM developed for the Kanto project
(Watanabe et al., 2008) and the Kyushu-GCM (e.g., Yoshikawa and Miyahara,
2005). This model uses important physical parameterizations for the MLT
region such as radiative transfer processes, including non-LTE and
solar radiative heating due to molecular oxygen and ozone. The effects of
ion drag, chemical heating, dissipation heating, and molecular diffusion are
also parameterized in the model. In this study, a standard-resolution JAGUAR
with a triangularly truncated spectral resolution of T42 corresponding to a
horizontal resolution of about 300 km (a latitudinal interval of 2.8125
Observation data used for the assimilation include the PREPBUFR global
observation dataset compiled by the National Centers for Environmental
Prediction and archived at the University Corporation for Atmospheric
Research (
The observation errors provided in the PREPBUFR dataset as a function of the
type of measurements and altitude
The MLS instrument onboard the Aura satellite was launched in 2004. The
satellite takes the polar orbit 14 times a day. Vertical profiles of several
atmospheric parameters are retrieved from a limb sounding of the thermal
emissions of the atmosphere. We used temperature data (v.4.2) retrieved from
the radiation of oxygen (
The horizontal intervals of the Aura MLS observation data along the track,
which is almost parallel to the meridional direction, are approximately
2
It has been suggested that the Aura MLS data include observation bias (e.g., Randel et al., 2016). In this study, a bias correction is performed, and the effect of the bias correction on the analysis data is examined. In addition to the retrieval quality flag information, a gross error check was applied in the quality control to exclude observations that are far from the first guess. The best settings for the gross error check are considered to be different between the mesosphere and lower atmosphere because of the different growth rates of model error in a specific period of time (e.g., a data assimilation window). Thus, the appropriate degrees of the gross error check are also examined.
The 4D-LETKF (Miyoshi and Yamane, 2007) is used as a data assimilation method. This method is an extension of the 3D-LETKF (Hunt et al., 2007), which includes the dimension of time (4D ensemble Kalman filter; Hunt et al., 2004). The base of the program used in this study has already been applied to many types of forecast models, such as the Global Spectral Model (GSM; Miyoshi and Sato, 2007), the Atmospheric GCM for Earth Simulator (AFES; Miyoshi et al., 2007), and the Non-hydrostatic Icosahedral Atmospheric Model (NICAM; Terasaki et al., 2015).
This section introduces the formulas used in the 4D-LETKF. The analyses,
forecasts, and observations are denoted by
The size of
The Kalman gain is simply written by using
The LETKF treats the analysis error covariance matrix,
When an analysis ensemble is derived, each ensemble takes its own time
evolution calculated by the forecast model, and the forecast at the next
step is derived by
Here we extend to a 4D analysis. By the modification of the observation
operator, the observation at any time (
The forecast at the time step
The EnKF initial condition is obtained using the time-lagged method as follows. First, a 6-month free run is performed from a climatological restart file for 1 June. The results from the free run over about 10 d with a center of 1 January are used as the initial condition for each ensemble member on 1 January. For the runs with 30 ensemble members, 30 initial conditions at a time interval of 6 h are used. For runs with 90 and 200 ensemble members, the time intervals for the initial conditions are taken as 4 and 2 h, respectively. The analysis data for the first 10 d of the assimilation are regarded as a spin-up and are hence not used to examine the assimilation performance.
As already mentioned, the parameter set of data assimilation usually made for the troposphere and stratosphere is not necessarily appropriate for the analysis when the MLT region is included. This is because the dominant physical processes and scales of motions could be different (e.g., Shepherd et al., 2000; Watanabe et al., 2008). This section describes the parameters that should be optimized for the data assimilation system for the whole neutral atmosphere from the troposphere up to the lower thermosphere. The relevance criteria of the data assimilation for each parameter are also described.
Parameter settings for sensitivity tests. Boldface shows the difference from the control (the first line). The control setting is equivalent to DB, P0.7, G20, L600, I15, W6, and M30.
The parameters included in the data assimilation system are divided into two categories. The first category includes two parameters describing the GCM: the horizontal diffusion coefficient and the factor of gravity wave source intensity in the gravity wave parameterization. The second category includes five parameters related to the data assimilation: the degree of gross error check, the localization length, the inflation factor, the length of assimilation window, and the number of ensembles. The sensitivity of the performance of assimilation is tested by changing one parameter among the standard set of the parameters as shown in Table 1. Finally, the performance of the assimilation with the best set of parameters is confirmed.
The criteria used for the evaluation of the data assimilation for each
parameter setting are observation minus forecast (OmF) and observation minus
analysis (OmA) in the observational space. One more criterion for examining
the quality of data assimilation is
In this section, two types of parameter sensitivity experiments are performed. One is a parameter tuning of the forecast model to reduce the systematic biases of the model in the MLT region. The other is an optimization of parameters related to the data assimilation module. Table 1 summarizes the experiments that we performed, and the best parameter set among them is shown as “Ctrl”. The grounds for regarding this parameter set as the best are described in detail in the following subsections. It is also worth noting that we tested many parameter sets other than those shown in Table 1 that did not work due to computational instability.
To reduce the model bias in the mesosphere, the vertical profile of the
horizontal diffusion coefficient and the gravity wave source intensity in
the non-orographic gravity wave parameterization are examined by comparing
observations in the summertime Antarctic mesosphere. Here, the zonal wind
observed by an MST radar called the PANSY radar in the Antarctic (Sato et
al., 2014) is used as a reference of the mesospheric wind. Note that the
temporal and longitudinal variation of the dynamical field is relatively
small in January and February in the summertime Antarctic mesosphere. The
model performance may depend on the parameters describing the MLT processes,
although we used default values of the model for this study. For example,
climatological concentrations of chemical species are used for the
calculation of the radiative heating rate, although the
The downscale energy cascade from resolved motions to unresolved turbulent motions is represented by numerical diffusion in most atmospheric models. A fourth-order horizontal diffusion scheme is used in the present version of the JAGUAR to prevent the accumulation of energy at the minimum wavelength. However, it is difficult to directly constrain the horizontal diffusion coefficient with observational data. In the present study, the horizontal diffusion coefficient is set to be constant up to the lower mesosphere and then exponentially increase above to reproduce realistic temperature and wind structures. As the horizontal diffusion in the model top is sufficiently strong to damp small-scale disturbances including (resolved) gravity waves, a sponge layer, which is usually included at the uppermost layers of GCMs, is not used in the model.
To optimize the tuning parameters of the forecast model, a series of free-run experiments with three different profiles of horizontal diffusion coefficients are performed. The impact of the difference in the horizontal diffusion coefficient is examined, focusing on the zonal mean zonal wind field. All experiments are started with the same initial conditions, which are obtained from a free-run simulation with climatological external conditions (hereafter referred to as “the climatological simulation”).
The vertical profiles of the horizontal diffusion coefficients given in the forecast model. Profile B was used for the data assimilation.
Figure 1 shows the three vertical profiles of the horizontal diffusion
coefficient. The horizontal axis denotes the
A free run was performed using the model with each diffusion coefficient
profile. The model fields at 00:00 UTC on 5 January of the climatological
simulation were used for the same initial condition for the three free-run
experiments. The results are examined for the zonal mean model fields
averaged over 40 d from 00:00 UTC on 12 January to 23:59 UTC on 20 February at
68.4
Vertical profiles of the zonal mean zonal wind averaged for the
time period of 12 January to 20 February from free runs with different
horizontal diffusions (A: green curves, B: red curves, C: blue curves)
for
It is also worth noting that the vertical axis in Fig. 2 denotes the geometric altitude. The log–pressure height vertical coordinate commonly used in GCM studies is approximately 5 km higher than the geometric height in the upper mesosphere at high latitudes. This difference is taken into account using the model's geopotential height as the vertical coordinate for comparison with the radar wind data, which are obtained as a function of geometric height.
The zonal wind for the experiment with the A profile is more eastward above 87 km and more westward below 85 km than observations. As a result, the vertical shear below 87.5 km is unrealistically strong. In contrast, the results of the experiments with the B and C diffusion profiles show similar profiles as the observations. The difference between the B and C experiments is observed in the vertical shear of zonal wind in the displayed upper mesosphere, which is large for B and small for C. The vertical shear is more realistic for B, although the wind magnitude itself is more realistic for C. We take B because this experiment has a zero-wind layer around 87 km, which is absent in the C experiment, as the zero-wind layer is an important feature observed in the upper mesosphere. We expect the model with the B diffusion coefficient profile to produce realistic vertical wind shear and hence potentially produce realistic wind fields including the zero-wind layer using the data assimilation.
The meridional cross sections of the zonal mean zonal wind
Figure 2d shows the results of the data assimilation experiments with the B
and C diffusion profiles for the time period of 12 January to 20 February 2017. The best set of parameters except for the diffusion profiles in
the data assimilation, which will be shown later in detail, was used for
these experiments. The results from the B experiment are more realistic in
the vertical shear and the location of the zero-wind layer than those of the
C experiment, although the difference is not large. Further comparison is
performed for the latitude–height cross section of zonal mean zonal wind and
Eliassen and Palm (E–P) flux (Fig. 3) from the data assimilation with the
B (left) and C (right) diffusion profiles. The meridional structures for the
zonal mean zonal wind and the E–P flux in the stratosphere are similar below
The source intensity in the model's non-orographic gravity wave parameterization is tuned as well. The amplitude of upward-propagating gravity waves increases with increasing altitude due to an exponential decrease in the atmospheric density. In the upper mesosphere, breaking gravity waves cause strong forcing to the background winds, which maintains the weak wind layer near the mesopause (Fritts and Alexander, 2003). As the gravity waves, which affect the mesosphere most in the summer, are non-orographically generated, we tuned the source intensity of the non-orographic gravity wave parameterization. It is expected that high source intensity lowers the wave breaking level and hence lowers the weak wind layer around the mesopause.
The vertical profiles of the zonal mean zonal wind averaged for
the time period of 12 January to 20 February from free runs with
gravity wave parameterizations of different source intensities (P0.5: green
curves, P0.7: red curves, P1.0: blue curves) for
The day–latitude section of MLS bias at
Figure 4a compares vertical profiles of the zonal mean zonal wind at
68.37
As we expected, the zonal mean zonal wind is weaker and the height of the zero-wind layer is lower for stronger source intensity. It seems that the zonal wind is weaker and the zero-wind layer is lower for P1.0 than those in the observations.
Figure 4d shows the results of the data assimilation experiments with P0.5, P0.7, and P1.0 for the time period of 12 January to 20 February 2017. For these experiments, the best set of parameters except for the source intensity was used in the data assimilation, which will be shown later in detail. Although all the profiles are consistent with observations within the standard deviation range, the profile for P0.7 is the most similar to observations in terms of the magnitude and the height of the zero-wind layer. From these results, we determined that the best source intensity is 0.7 times the original one (i.e., P0.7).
According to the Aura MLS data quality document (Livesey et al., 2018), the
MLS temperature data have a bias compared to the SABER ones as a function of
the pressure, which is
In this study, the MLS observation bias is first estimated as a function of the calendar day at each latitude and each pressure in a range of 177.838 to 0.001 hPa. As the reference for the correction, we used the TIMED SABER temperature data (v.2.0), which are considered to have little observation bias, at least in the altitude range from 85 to 100 km, as confirmed by Xu et al. (2006), who used data from the sodium lidar at Colorado State University, providing the absolute value of the temperature. Xu et al. (2006) attributed the disagreement below 85 km to high photon noise contaminating the lidar observations. Thus, we used the SABER temperature data for the Aura MLS bias estimation in the height range of 10–100 km.
The observation view of SABER is altered every
The bias is estimated using data from 2005 to 2015. The original vertical
resolution of MLS (
The vertical profile of the global average of the Aura MLS temperature bias (the solid black curve) with standard deviation (gray shading). Error bars denote reported bias (Livesey et al., 2018).
Figure 5 shows the estimated MLS bias as a function of calendar day and
latitude at 10, 1, 0.1, and 0.01 hPa. The MLS bias shows a strong dependence
on the altitude and latitude and has an annual cycle with amplitudes of 2 to
4 K. Figure 6 shows the vertical profiles of global mean Aura MLS bias along
with the bias reported in the data quality document (Liversey et al., 2018).
For example, the global mean MLS biases estimated by the present study are
The meridional cross sections of zonal mean temperature
To evaluate the effect of the bias correction, data assimilation was performed using the MLS data with and without bias correction. Figure 7 compares the latitude and pressure section of the zonal mean temperature and zonal wind between the two analyses. The difference in zonal mean temperature between the two (Fig. 7c) resembles the corrected bias (Fig. 7d). In contrast, the difference in the zonal mean zonal wind is not very large (Fig. 7g). This is because the latitudinal difference in the bias, which largely affects the zonal mean zonal wind through the thermal wind balance, is not large compared to the vertical difference. In our study, the bias correction of the MLS data is made before the data assimilation, as in standard assimilation parameter setting.
A series of sensitivity tests were performed to obtain the best values of each parameter in the data assimilation system with 30 ensemble members. This number of members is practical for the data assimilation up to the lower thermosphere with current supercomputer technology. The examined assimilation parameters are the gross error coefficient, localization length, inflation coefficient, and assimilation window length. The best parameter set obtained by the sensitivity tests is denoted by Ctrl in Table 1. There are six assimilation parameters to be examined. We performed an assimilation run with almost all combinations of the parameters. Several parameter settings did not work due to computational instability. We found a parameter set that provides the best assimilation results in our system. This best parameter set is placed as the control setting (Ctrl), and the parameter dependence of the assimilation performance is examined by using the results in which one of the parameters is changed from the Ctrl set. Section 3.3.5 gives a short summary of the data assimilation setting optimization for 30 ensemble members.
The gross error check is a method of quality control (QC) for the observation data used for the assimilation. In this method, an observation is assimilated only if its OmF is smaller than expected, assuming that the forecast model provides a reasonable representation of the true atmosphere. In many previous studies, observations are not assimilated when the OmF exceeds 3–5 times the observational error for the troposphere and stratosphere. However, this criterion may not be suitable for the mesosphere and lower thermosphere, in which the systematic bias and predictability of the model are likely higher and lower, respectively (e.g., Pedatella et al., 2014a). Thus, the maximal allowable difference between the MLS observations and model forecasts normalized by the observational error, which is called the “gross error coefficient”, is set at 20 (hereafter referred to as the G20) for the MLS measurements as a control experiment of the present study, whereas it is set at 5 for the PREPBUFR dataset as in previous studies such as Miyoshi et al. (2007). Consequently, this setting uses most of the MLS observations to correct the model forecast. To investigate the effect of the enlarged gross error check coefficient, the result for the G20 is also compared to the experiment with the gross error coefficient of 5 for the MLS measurement (G5). Note that the other parameters in addition to the gross error coefficient are taken to be the same for the G20 (Ctrl) and G5 (see Table 1).
Histogram of the OmF (thin curves) and OmA (thick curves) at 0.1 hPa
Figure 8 compares the histograms of the OmF (a gray curve) and OmA (a black curve) for the G20 (left) and G5 (right) experiments at 0.1, 1, and 10 hPa. For both settings, the mean OmF values are slightly negative, whereas both the mean bias and standard deviations of the OmA are smaller than those of the OmF at most pressure levels. As expected, the OmF is more widely distributed for the G20 than for the G5. This reflects the inclusion of more observations for the assimilation with the G20. Although the OmF distribution for the G20 is close to the normal distribution, the distribution of for the G5 seems distorted, probably by an overly strict selection of observations close to the model forecasts, which can be seen from the number of assimilated observations, as indicated by the area of the histogram in Fig. 8, which is only a half or a third the number for the G20.
Figure 9 shows vertical profiles of the mean OmF, OmA, and
The vertical profiles of the global mean
The vertical profiles of the global mean
In the LETKF, the observation error is weighted with the inverse shape of
the Gaussian function (observational localization) of the distance (
A sensitivity test is performed by taking
The localization length dependence of the root mean square (RMS) difference (K) between the analysis temperature and the MLS temperature observation. The averaged data for the time period of 12 January to 20 February 2017 are shown.
This result suggests that the best localization length depends on the height. To see the height dependence in a different way, the root mean square (RMS) of the temperature difference from the (bias-corrected) MLS observations was calculated for each experiment at each height. Results are shown in Table 2 for typical levels of 10, 1, 0.1, 0.01, and 0.005 hPa in the stratosphere and mesosphere. A smaller RMS means that observations are better assimilated. The RMS is smallest for the L300 at lower levels of 10 and 1 hPa, for the L600 at 0.1 hPa, and for the L1000 at upper levels of 0.01 and 0.005 hPa, suggesting that optimal localization length depends on the height.
Based on the results, we employed the L600 as the best
To avoid possible underestimations in the forecast error covariances due to
the small number of ensembles used in the assimilation, a covariance
inflation technique is employed (see Eq. 9). The inflation coefficient is
generally set to
Figure 11 shows meridional cross sections of the zonal mean ensemble spread of temperature for each assimilation run. The ensemble spread for the I7 is about 1 K at most in the mesosphere and lower thermosphere, which is smaller than the observation accuracy (1–3 K). In contrast, the ensemble spreads for the I15 and I25 are distributed in the range of the observation accuracy. The necessity of a larger inflation coefficient is likely due to the large diffusion coefficient in the upper mesosphere and lower thermosphere used in the forecast model (Fig. 1). However, a larger inflation coefficient leads to an unrealistically thin vertical structure of ensemble spreads in the lower mesosphere, which is conspicuous for the I25 (Fig. 11). Figure 12 shows the time series of the global mean temperature spreads for respective settings at 0.01 and 10 hPa. The temperature spreads vary slightly in time and seem stable after 13 January for both pressure levels.
The meridional cross section of the zonal mean ensemble spread of
temperature (K) for
The time series of the global mean temperature spread for
The vertical profiles of the mean OmF, OmA, and
Interestingly, the range of the best inflation coefficient also depends on
the height from a viewpoint of
The length of the assimilation window, which is a time duration of forecast
and observation to be assimilated during one assimilation cycle, is also
examined. When the assimilation window is set to 6 h, the forecast is first
performed for
A longer window has the advantage that more observations are assimilated at
once, while taking the predicted physically balanced time evolution of
dynamical fields into account. However, the longer forecast length may
increase model errors. Moreover, the 4D-EnKF assumes a linear time evolution
of the dynamical field during the assimilation window length. Thus,
variations with strong nonlinearity or with timescales shorter than the
assimilation window length are not taken into account. We tested
assimilation windows of 3 h (W3), 6 h (W6, Ctrl), and 12 h (W12) (see Table 1). The W12 (W3) assimilation was performed using the forecasts for
The vertical profiles of the global mean
The vertical profiles of the global mean
Figure 14 shows the vertical profiles of the mean OmF, OmA, and
The bias of the time series of zonal mean temperature at 70
In Sect. 3.3.1 to 3.3.4, a series of sensitivity tests for each parameter
in the data assimilation system with 30 ensemble members was performed as
shown in Table 1. Figure 15 shows the time series of the zonal mean
temperatures at 70
The Ctrl time series is also quite similar to that of MERRA-2 in spite of
the small number of ensemble members, including drastic temperature change
during the major SSW event, although a warm bias of
The EnKF statistically estimates the forecast error covariance using
ensembles. A large ensemble size (i.e., a large number of ensemble members)
is favorable because it reduces the sampling error of the covariance and
improves the quality of the analysis. However, the ensemble size has a
practical limit related to the allowable computational resources. An
ensemble size of
The time series of the zonal mean temperature at 70
The vertical profiles of the global mean
Figure 16 shows the vertical profiles of the mean OmF, OmA, and
In the following, an attempt is made to estimate the minimum number of
ensemble members as a function of height using forecasts of ensemble members
from the M200 experiment because 90 is a sufficient number for high-quality
assimilation, judged from the similarity of the performances of the M90 and
M200 runs. Figure 17 shows the correlation coefficient of forecasts at each
longitude for a reference point of 180
An example of ensemble correlation of temperature. Results for
40
An example of the RMS of spurious correlation. Results for
40
The RMS of the spurious correlation in the region outside the meaningful
correlation region is used to estimate the minimum optimal number of
ensemble members. The RMS is examined as a function of the number of
ensemble members. Each edge longitude of the meaningful correlation region
is determined where the correlation falls below 0.1 nearest the reference
point, which are 171.6
The vertical profiles of the minimum number of required ensemble
members that were estimated from the RMS of spurious correlation. The black,
dark gray, and light gray curves show the results for the Equator,
40
Figure 19 shows the minimum optimal number of ensemble members as a function
of the height for 40
This paper gives the first results of the 4D-LETKF applied to the GCM that
include the MLT region. Thus, to examine the performance of our
assimilation system, the best result obtained from the M200 run among the
assimilation experiments is compared with MERRA-2 as one of the standard
reanalysis datasets. First, we calculated the spatial correlation of the
geopotential height anomaly from the zonal mean as a function of the
pressure level and time (Fig. 20). The correlation is higher than 0.9
between
The zonal mean of the spatial correlation of the geopotential height anomaly from the zonal mean between the analysis (M200) and MERRA-2. Contours of 0.5, 0.6, 0.7, 0.8, 0.9, 0.95, 0.97, and 0.99 are shown.
The meridional cross section of the zonal mean temperature (
Location, radar type, and vertical resolution used for the comparison with the analysis. “MST radar” stands for the mesosphere–stratosphere–troposphere radar.
Next, the zonal mean zonal wind and temperature in the latitude–height
section from our analysis and MERRA-2 are shown for the time periods before
the major warming onset (i.e., 21–25 January) and after (i.e., 1–5 February) (Fig. 21). A thick horizontal bar shows the 0.1 hPa level up to
which MERRA-2 pressure level data are provided. The overall structures of
the two datasets are similar: the stratopause in the northern polar region
is located at a height of
The winds obtained from the M200 assimilation experiment are also compared
with wind observations by meteor radars at Longyearbyen (78.2
The time series of the zonal
Strong fluctuations with time-varying amplitudes are observed for both zonal
and meridional radar winds for each station. The dominant time period is
longer at Kototabang in the equatorial region than that of
In contrast, some consistency is observed for relatively long-period variations (periods longer than several days). At Longyearbyen, the slowly varying zonal wind component is slightly positive before 31 January and significantly positive from 1 to 6 February, while the slowly varying meridional wind tends to be significantly negative in the time period of 28–31 January. At Kototabang, the slowly varying zonal wind tends to be slightly negative before 29 January and almost zero afterward, while the slowly varying meridional wind is almost zero throughout the displayed time period. At Syowa Station, the slowly varying zonal wind tended to be negative from 23 to 30 January and after 2–5 February, while the slowly varying meridional wind tends to be positive from 24 to 31 January.
There are several plausible causes for the discrepancy in short-period variations. First, there may be room to improve the model performance to reproduce such short-period variations. Second, the Aura MLS provides data along a sun-synchronous orbits, and hence fluctuations associated with migrating tides may be hard for it to capture. Third, a large local increment added by the assimilation of the MLS data may cause spurious waves in the model. Fourth, there may be inertia–gravity waves with large amplitudes in the upper mesosphere (e.g., Sato et al., 2017; Shibuya et al., 2017), which cannot be captured with the relatively low-resolution GCM.
A new advanced data assimilation system employing a 4D-LETKF method for the height region from the surface to the lower thermosphere has been developed using a GCM with a very high top that we called JAGUAR. Observation data from NCEP PREPBUFR and Aura MLS that covered the whole neutral atmosphere up to the lower thermosphere were used for the assimilation. The time period focused on by the present study was 10 January to 28 February 2017. This period includes a major SSW event that occurred on 1 February in the Arctic, for which an international observation campaign for the troposphere, stratosphere, and mesosphere was performed using a radar network.
Before optimizing the parameters of the data assimilation system, the vertical profile of the horizontal dissipation and source intensity of the non-orographic gravity wave parameterization used in JAGUAR were tuned by comparing them to the vertical profiles of gradient winds estimated from the MLS temperature and horizontal winds observed by the PANSY radar. The observation bias in the MLS temperature data was estimated using the SABER temperature data and subsequently corrected.
By performing a series of sensitivity experiments, the best values of the other parameters were obtained for the data assimilation system using 30 ensemble members as a practical assimilation system for the middle atmosphere. The best parameter set is called the Ctrl experiment in Table 1. The optimized value for each parameter in the assimilation of the atmospheric data up to the lower thermosphere was different from those used for the standard model covering the troposphere and stratosphere. There are several possible reasons for these differences: first, the model performance is not very mature for the MLT region. Second, the number of observation data and observable quantities are limited for the MLT region. Third, the dominant disturbances (and dynamics as well) are different from those in the lower atmosphere. Because of the first and second reasons, it is better to take a larger gross error check coefficient in order to include a larger percentage of the observation data. It was shown that the optimal localization length depends on the height: a smaller localization length is better for lower heights. Thus, the best length for the middle of the model altitude range (i.e., 0.1 hPa) was employed in the best parameter set. It was also shown that the inflation factor should be larger than for the standard model, although overly large factors do not give stable ensemble spreads. A shorter assimilation window seemed better for the MLT region, which is probably due to the dominance of short-period disturbances, such as quasi-2 d waves and tides. However, shorter assimilation windows have a problem. The number of available observation data becomes small and the analysis thus tends to be more reflected by the model forecasts that are not as mature as those for the lower atmosphere.
In addition, a minimum optimal number of ensemble members was examined using the results with an assimilation system of 200 ensemble members based on the erroneous ripple of correlation function. The minimum optimal number of ensemble members slightly depends on the height: about 100 members below 80 km and 150 members above. It should be noted, however, that the introduction of the finite localization length to the assimilation may work to avoid spurious correlation at distant locations even with a lower number of ensemble members than the optimal number.
The validity of the data obtained from our assimilation system was examined
by comparing the MERRA-2 reanalysis dataset that has the highest top among
the currently available reanalysis datasets. The correlation was greater
than
In future work, we plan to use more observation data in the middle atmosphere for the assimilation. These include satellite data, such as temperature observation data from SABER, radiance data from the SSMIS, and Global Navigation Satellite System (GNSS) radio occultation data, as well as wind data from radars in the mesosphere. We also plan to examine the impact of assimilating these data with observation system simulation experiments using simulation data from a high-resolution GCM. The predictability of the GCM will also be studied in the near future.
Here we show the equivalence of the two methods, namely the calculation of
time development after the data assimilation and the 4D data assimilation
with the calculation of time development. The case of
Similarly, the analysis error covariance
The source codes for the data assimilation are available for the editor and
reviewers. The copyright of the code for LETKF belongs to Takemasa Miyoshi,
and the related code can be accessed from
Meteor radar data from Kototabang are available at the Inter-university
Upper atmosphere Global Observation NETwork (IUGONET) site
(
DK and KS designed the experiments, and DK carried them out. SW developed the forecast model (JAGUAR) code. KM implemented the data assimilation module into JAGUAR. KS and DK prepared the paper with contributions from all the coauthors.
The authors declare that they have no conflict of interest.
We greatly appreciate Takemasa Miyoshi, Tomoyuki Higuchi, and Hiromichi Nagao for fruitful discussion and also Masaki Tsutsumi and Chris Hall for providing the meteor radar data from Longyearbyen. The data assimilation experiments were performed using the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) Data Analyzer (DA) system. Part of this work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. PANSY is a multi-institutional project with core members from the University of Tokyo, the National Institute of Polar Research, and Kyoto University. The PANSY radar measurements at Syowa Station are operated by the Japanese Antarctic Research Expedition (JARE). The figures were produced by the GFD-DENNNOU Library. We thank two anonymous reviewers for their constructive comments.
This research has been supported by the JST CREST (grant no. JPMJCR1663) and the JSPS KAKENHI (grant no. 18H01276).
This paper was edited by Josef Koller and reviewed by two anonymous referees.