Abstract

The NCAR Whole Atmosphere Community Climate Model (WACCM) is used to investigate the dynamical influence of the lower and middle atmosphere on the upper mesosphere and lower thermosphere. In simulations using a methodology adapted from the “specified dynamics” (nudged) version of the model, horizontal winds and temperature over part of the vertical range of the atmosphere are relaxed toward results from a previous simulation that serves as the true simulation, equivalent to meteorological analysis. In the upper mesosphere, the magnitude of the divergence of the constrained simulations from the true simulation depends on the vertical extent and frequency of the data used for nudging the model and grows with altitude. The simulations quantify the error growth of the model dynamical fields when data and forcing terms are known exactly and there are no model biases. The error growth rate and the ultimate discrepancy between the nudged and true fields depend strongly on the method used for representing gravity wave drag. The largest error growth occurs when the gravity wave parameterization uses interactive wave sources that depend on convective activity or fronts. Errors are reduced when the same parameterization is used with smoothly varying specified wave sources. The smallest errors are seen when the parameterized gravity wave drag is replaced by linear Rayleigh friction damping on the wind speed. These comparisons demonstrate the role of gravity waves in transporting the variability of the troposphere into the mesosphere and lower thermosphere.

1. Introduction

Observations show that signatures from the troposphere and stratosphere can be detected in the mesosphere, thermosphere, or ionosphere. Examples include variation of tides in the ionosphere (Goncharenko et al. 2010) and ozone in the upper mesosphere (Smith et al. 2009) associated with sudden stratospheric warmings, nonmigrating tides tied to latent heating in the troposphere (Hagan and Forbes 2002; Immel et al. 2006), and gravity waves in the thermosphere (Nicolls et al. 2014) and ionosphere (Bishop et al. 2006) linked to tropical cyclones. The thermosphere and ionosphere also respond to variable energy and particle input from the sun and from the magnetosphere. The balance between dominance of forcing from below and from above can vary depending on the magnitudes of the perturbations.

Above the tropopause, much of the atmospheric variability is associated with upward-propagating waves, including planetary waves, tides, and gravity waves. The sources and propagation of many of these waves depend on the global-scale or synoptic-scale meteorology in the troposphere and stratosphere. This is the basis of attempts to use global atmospheric models to simulate realistic day-to-day variations in the mesosphere and thermosphere by constraining the model dynamical fields in the troposphere and stratosphere, where these fields are well determined by abundant observations.

Early three-dimensional global modeling of the mesosphere and thermosphere historically used models with simulation domains that did not include the lower atmosphere (e.g., Roble and Ridley 1994; Fuller-Rowell and Rees 1980). Vertical domains in current global high-top models extend from Earth’s surface to upper boundaries ranging from the upper mesosphere to the upper thermosphere (Schmidt et al. 2006; Eckermann et al. 2009; Liu et al. 2010; Akmaev 2011; Ren et al. 2011; Jin et al. 2012; Marsh et al. 2013). Most state-of-the-art high-top models include a facility for constraining the dynamical fields with observations or observation-based reanalyses over part or all of the model domain. The constraints are performed by nudging (relaxing with a specified time constant) to global reanalysis fields or by assimilating observational data.

There are several reasons that simulations with constraint are used. One is that a model simulation whose dynamical fields correspond to observations during a specific period gives an important tool for evaluating chemical composition, response of the atmosphere to external forcing, and other topics for which it is advantageous to minimize differences in dynamical evolution. Another is that comparisons between model simulations and observations are facilitated when the same temporal variability is present in both. However, constraining some of the model fields in the lower or middle atmosphere does not guarantee that the simulation will closely match the dynamical observations in the upper atmosphere. Pedatella et al. (2014a) compared the thermospheric simulations from four constrained models whose domains extend at least into the lower thermosphere. They found that there was a wide discrepancy among model simulations in terms of both the zonal-mean state and semidiurnal tide variations during a sudden stratospheric warming.

Until recently, the region where the constraint was applied was limited to the troposphere and stratosphere, where meteorological data and analyses have sufficient observational input to provide reliable values (Polavarapu et al. 2005). As data coverage in the mesosphere has improved because of observations from long-lived research satellites, it is now possible to apply the constraints to a much more extensive depth of the atmosphere. The release of the MERRA-2 data (Bosilovich et al. 2015), which assimilates additional observations, including temperature observations from the Microwave Limb Sounder (MLS) up to 0.01 hPa beginning in 2004, is one such example that is now available for nudging. The research applications of constraining over a wide depth by nudging or data assimilation can be seen in several recent papers (Eckermann et al. 2009; Pedatella et al. 2014b; Siskind et al. 2015). However, there are also applications for continuing the use of constraints over a more limited vertical range. Simulations constrained over a limited altitude domain can be used to investigate the extent to which variability that extends upward from the troposphere and stratosphere affects or controls the dynamics of the mesosphere and lower thermosphere (MLT).

In the present study, we focus specifically on addressing the limits to the dynamical control of the MLT by the dynamical activity in the troposphere and stratosphere. We look at factors that have a limiting impact on predictability of the MLT. We can consider two hypothetical extremes. In one, the unpredictability of the MLT is “homegrown” in the sense that failures in predictability arise in situ in a manner similar to the chaotic divergence in the troposphere (Lorenz 1969; Durran and Weyn 2016). In the other extreme, uncertainties in the MLT are introduced by upward propagation of uncertainties in the troposphere associated with incomplete or inaccurate specification of dynamical fields.

We use a high-top model to investigate the impact that nudging has on the simulated dynamical fields both within the nudged region and in the overlying atmosphere. The goal is to characterize the impact of dynamical evolution in the troposphere and stratosphere on the dynamics of the MLT. The model experiments are idealized to isolate the impact of known dynamical fields on the resolved dynamics of the MLT.

2. Description of the model and the dynamical constraints

a. WACCM

The present study uses the Whole Atmosphere Community Climate Model (WACCM), which is one of the atmospheric model options for NCAR’s Community Earth System Model (CESM). WACCM extends from Earth’s surface to about 140 km and simulates the interactions of dynamics, chemistry, and energetics. WACCM is freely available and has been used for a number of middle-atmosphere studies. This study uses version 4 of WACCM [see Marsh et al. (2013) for a description of the basic model and its performance]. WACCM4 standard horizontal resolution is 2.5° × 1.9° (longitude × latitude). There are 66 pressure levels with a spacing of approximately 1.1–1.75 km in the troposphere and stratosphere and 3.5 km in the mesosphere and thermosphere. The model top is at 5.9 × 10−6 hPa, about 140 km. Solomon et al. (2015) provide updates to the model chemistry.

All of the simulations described here begin on 1 January 2006 and run for 45 days. They are initialized from a free-running simulation and therefore do not resemble the dynamical events observed during that particular winter. There is no major sudden stratospheric warming in the simulations, although there are several minor warmings.

WACCM can be set up with different options for interaction. In the current study, we use two options. The “free running” model used here includes specified monthly varying sea surface temperatures and sea ice distributions based on observations; with this option, there is no interaction between the atmosphere and ocean. Chemical and dynamical fields interact through transport and radiative transfer. A feature of free-running models is that the meteorological conditions diverge for minor differences in the initial conditions (Liu et al. 2009). This aspect has been exploited for performing multiple realizations to assess uncertainties in the predicted atmospheric response to climate forcing.

The other setup option used in this study is the nudged option of WACCM, which is called “specified dynamics” (SD) and is commonly known as SD-WACCM. The horizontal winds, temperature, surface pressure, and surface fluxes are constrained at each model time step over a specified pressure range by relaxing to a specified meteorological data field (e.g., Kunz et al. 2011; Lamarque et al. 2012). In the usual application of the SD process in WACCM, the vertical range for the nudging is from Earth’s surface to 50 km, and the strength of the nudging is relaxed linearly to zero over the 10 km above. The meteorological fields for relaxation are then taken from a standard meteorological analysis or reanalysis field and are defined at every model grid point within the nudging domain. Meteorological fields are typically updated at intervals of 6 h; to get fields for nudging at intervening time steps, the variables are interpolated between the two bracketing times.

b. The nudging process

Consider the determination of Tn, the temperature at the nth model time step:

 
formula

The predicted temperature depends on the temperature at the previous time step Tn−1 and the temperature tendencies from advection, diabatic and adiabatic processes, and diffusion. In the free-running model,

 
formula

while in the nudged model,

 
formula

where Tmet is the meteorological data used for nudging and α is a small fraction. In the standard setup, the SD-WACCM time step is 0.5 h and α = 0.001, giving a relaxation time of about 50 h. Note that Tmet is linearly interpolated to the model time step n.

The time step of the meteorological fields in Eq. (3) is n; if α is set to 1, the model fields are overwritten by the meteorological fields at that time step. However, for α < 1, Tmet enters the equation weighted against Tn−1, not Tn. This can be seen by expanding Eq. (3):

 
formula

This time offset between the n − 1 time step (for the model prediction) and the nth time step (for the meteorological data) is not negligible in a model such as WACCM, which is run with a time step of 0.5 h. However, the errors introduced by this time step offset are expected to be small compared to the errors introduced by biases in WACCM climatological wind and temperature fields.

In WACCM, there is no weighting of the nudging parameters based on the difference in time; α in Eq. (2) is constant over all time steps. The value of α is also constant over all longitudes and latitudes and, as indicated above, has a simple taper in altitude. Although the nudging was developed for use with meteorological analyses, the process can in principle be used for nudging to any other global gridded analyses or model data.

c. Model simulations

In the present study, we first run WACCM in the free-running mode and save data at 1-h intervals. Then these data are used to nudge specified dynamics runs for which the initial conditions are slightly perturbed from the base case. The perturbation is applied by adding a random amount, varying at every grid point, with magnitude between +0.1 and −0.1 m s−1, to zonal wind speeds below 100 hPa. Although this perturbation is smaller than the uncertainty in wind speeds from typical gridded data based on observational analyses, it is sufficient to make simulations begin immediately to diverge. With this, we can define the “exact” or “true” atmospheric state as that simulated by the free-running case used to generate the meteorological fields for nudging. Comparison of the nudged and free-running simulations gives us a way to assess how closely the nudged atmosphere conforms to the true case. All simulations begin on 1 January 2006.

In these model experiments, a number of sources of variability that affect comparisons of model simulations with observations are absent. In other words, these are perfect model experiments. Both the meteorological fields used for nudging (i.e., those saved from the free-running model) and the nudged cases have exactly the same physics. Likewise, the meteorological fields used for nudging are exact and have no errors. All external forcings, such as solar variability and ocean changes, are specified and are identical in all of the simulations. As a result, the RMS differences between fields in two model simulations do not include any appreciable climatological bias, as is usually present in differences between a simulation and an observational dataset, reanalysis data, or simulations from another model. Having defined the perfect model allows us to focus specifically on the primary question we are addressing: how much does the dynamical evolution of the troposphere and stratosphere control the MLT?

In addition to the simulations using the standard WACCM4 routines, we repeat a subset of the simulations with different schemes for representing gravity wave drag, as described in section 3b. For each set of simulations using the same gravity wave scheme, the base (true) simulation, the alternative free-running simulations, and the nudged simulations all use the same model code. The three gravity wave drag schemes are 1) the version from WACCM4, which has interactive sources of convectively generated and frontally generated nonorographic gravity waves (Beres et al. 2005; Richter et al. 2010), 2) the version from WACCM3, which uses specified tropospheric sources of nonorographic gravity waves (Garcia et al. 2007), and 3) Rayleigh friction, which represents gravity wave drag by a linear damping on the horizontal wind.

Table 1 lists the simulations that are discussed in the following sections. The altitude given for the upper limit of the nudging domain indicates the range for full nudging; that is, nudged <50 km indicates full nudging from the surface to 50 km with a taper to zero between 50 and 60 km.

Table 1.

WACCM simulations: (left to right) the names used to refer to the runs and information about whether the setup is free running (FR) or nudged (SD), the depth of the nudging region, the frequency at which meteorological data are available, and which gravity wave (GW) parameterization was used in the simulation.

WACCM simulations: (left to right) the names used to refer to the runs and information about whether the setup is free running (FR) or nudged (SD), the depth of the nudging region, the frequency at which meteorological data are available, and which gravity wave (GW) parameterization was used in the simulation.
WACCM simulations: (left to right) the names used to refer to the runs and information about whether the setup is free running (FR) or nudged (SD), the depth of the nudging region, the frequency at which meteorological data are available, and which gravity wave (GW) parameterization was used in the simulation.

3. Error growth

a. RMS error using standard WACCM4 physics

We first run the base free-running simulation for 45 days beginning 1 January and store the results as the “true” situation in a form that can be used for nudging future runs. We also run two other free-running realizations with small random differences in initial tropospheric zonal wind speeds of less than 0.1 m s−1. The nudged cases use four different altitude ranges over which nudging is applied, as given in Table 1. These simulations use the standard WACCM4 representation of gravity wave drag.

Errors and error growth are quantified using the instantaneous root-mean-square (RMS) differences of each simulation from the true simulation at the same time step. To focus on the mesosphere, the temporal evolution of the daily global RMS error at 0.004 hPa (about 85 km) is used to illustrate the divergence between different simulations. The global RMS error between the nudged and the base simulations is calculated using the model fields at every longitude and latitude for each hour during the day. Figure 1 shows a comparison of the global RMS errors in the free-running simulations and all of the simulations using the standard WACCM parameterized gravity wave drag and diffusion (see Table 1). For the solid curves, the meteorological data are updated every hour, while for the dashed curves the meteorological fields are updated every 6 h. The two free-running simulations use different random perturbations to the tropospheric zonal wind fields, as described in section 2c.

Fig. 1.

RMS error at 0.004 hPa (approximately 85 km) of (top) temperature (K) and (bottom) zonal wind (m s−1) for the first 45 days of 10 model runs. The colors indicate the height to which the full nudging is applied. Solid colored curves are for nudging to meteorological fields available every hour, and dashed curves are for nudging to meteorological fields available every 6 h. The black curves are for free-running simulations with slightly different initial conditions.

Fig. 1.

RMS error at 0.004 hPa (approximately 85 km) of (top) temperature (K) and (bottom) zonal wind (m s−1) for the first 45 days of 10 model runs. The colors indicate the height to which the full nudging is applied. Solid colored curves are for nudging to meteorological fields available every hour, and dashed curves are for nudging to meteorological fields available every 6 h. The black curves are for free-running simulations with slightly different initial conditions.

It is evident that, for free-running simulations, the simulated temperature and zonal wind fields diverge at a steady rate for about 25 days and then reach a steady difference of about 13 K and 40 m s−1, respectively. This growth in error is similar to that found by Liu et al. (2009) using an earlier version of WACCM. The nudged fields all reach a plateau that has a smaller RMS error than that of the free-running cases. The global RMS error is smallest when the nudging is applied all the way through the middle atmosphere. Note that, for the case in which nudging is extended to 125 km, the RMS error shown in Fig. 1 is assessed at an altitude that is itself nudged. Figure 1 clearly shows that the error increases when the upper limit of the nudged region is lower in the atmosphere. The minimum altitude range for nudging in these simulations is full nudging to 15 km, which is then tapered off between 15 and 25 km. For this case, for which all of the troposphere and part of the lower stratosphere are constrained, there is a small reduction in the eventual error over a free-running simulation after the first 10 days (cf. the blue to the black curves).

It is also evident from Fig. 1 that the global RMS error is reduced when the meteorological data used for nudging is incorporated every hour rather than every 6 h. The standard (used for WACCM) is every 6 h, based on the availability of the observation-based reanalysis meteorological fields that are used.

Figure 2 shows the global RMS error as a function of pressure averaged over days 30–40 of each simulation. The RMS error for all SD simulations grows in the mesosphere beginning at about 1 hPa even when the model is nudged above there (the red and orange curves). Also note the green dashed line, which shows the error growth for a simulation nudged with 6-hourly data up to 50 km. This is most similar to the standard setup for SD-WACCM. In the mesosphere above about 0.1 hPa, this nudging leads to a substantial RMS error. The reduction of the RMS error from a free-running case is only 50% (cf. the green dashed line to the two solid black lines) even in our idealized simulation, in which the fields used for nudging are free of errors and biases and are available at every horizontal grid point.

Fig. 2.

RMS error of 10 model runs averaged over days 30–40 of (top) temperature (K) and (bottom) zonal wind (m s−1) as a function of pressure. The colors indicate the height to which the full nudging is applied. Solid colored curves are for nudging to meteorological fields available every hour, and dashed curves are for nudging to meteorological fields available every 6 h. Black curves are for free-running simulations.

Fig. 2.

RMS error of 10 model runs averaged over days 30–40 of (top) temperature (K) and (bottom) zonal wind (m s−1) as a function of pressure. The colors indicate the height to which the full nudging is applied. Solid colored curves are for nudging to meteorological fields available every hour, and dashed curves are for nudging to meteorological fields available every 6 h. Black curves are for free-running simulations.

The RMS error includes errors due to small-scale differences, such as slight shifts in the amplitude or phase of waves and tides, as well as broader differences, such as the daily and zonally averaged temperature and winds. For Fig. 3, the RMS errors are determined from the daily zonal-mean temperature and zonal wind; the errors are then averaged over days 30–40. The results are shown for all latitudes and for latitudes poleward of 70°N, which is the most variable part of the atmosphere during this northern winter period. The global RMS errors of the daily zonal averages are approximately one-third of the global errors for individual time steps and grid points (note the difference in the axes from those in Fig. 2). The RMS errors for winter high latitudes are substantially larger than the global errors. In contrast to the global-mean RMS error using all grid points at every hour (Fig. 2), the global and high-latitude winter RMS errors for the nudged simulations in Fig. 3 grow much more slowly with altitude above the lower mesosphere.

Fig. 3.

As in Fig. 2, but for error of the (top) global and (bottom) high-northern-latitude (poleward of 70°N) daily and zonally averaged fields. Only cases nudged with 1-h meteorological data are shown.

Fig. 3.

As in Fig. 2, but for error of the (top) global and (bottom) high-northern-latitude (poleward of 70°N) daily and zonally averaged fields. Only cases nudged with 1-h meteorological data are shown.

Liu et al. (2009) attributed the rapid error growth in WACCM3 to resolved gravity waves in the model. Their analysis indicated that error growth was smaller when the troposphere was constrained by periodic reinitialization. However, both the low improvement in skill in the current simulations when the constraint is applied below 15 km and the rapid increase of global RMS error with altitude indicate that the tropospheric constraint is not sufficient to keep the MLT fields close to the true atmosphere in this version of WACCM. The mechanism for this is explored in section 3b.

For about 10 days at the beginning of the simulations, the error growth is larger in the nudged simulations than in the free-running simulations (see Fig. 1). We consider several possible reasons for this: 1) the nudging process creates an imbalance that leads to the generation of resolved gravity waves, as seen in the Liu et al. (2009) simulations; 2) the temporal interpolation of the meteorological data in the nudged simulations affects the phase of atmospheric tides, which are then offset from the tides generated spontaneously in WACCM; or 3) the nudging process causes offset in dynamical fields, as suggested by the formulation for nudging in Eq. (4).

The basis for the first potential mechanism is that the imbalances caused by the nudging process could lead to the triggering of resolved gravity wave modes. We would expect such gravity wave modes to be seen in a broad range of scales, not restricted to the large scales. Figure 4 shows the error growth at two levels broken down by zonal wavenumber for a nudged simulation (nudged to 50 km using 1-h meteorological data) and one of the free-running simulations. It is clear from this figure that error growth in both simulations is highest at the largest scales. Rather than improving the agreement between the nudged and true simulations, the nudging itself is contributing to error growth of the large-scale dynamical fields. This comparison suggests that resolved gravity waves are not the dominant process leading to the rapid error growth of nudged simulations.

Fig. 4.

Global average RMS error of temperature (K) at (top) 0.3 and (bottom) 0.004 hPa as a function of time and zonal wavenumber for the first 8 days of two model simulations: nudged to 50 km with (left) 1-h data and (right) free running.

Fig. 4.

Global average RMS error of temperature (K) at (top) 0.3 and (bottom) 0.004 hPa as a function of time and zonal wavenumber for the first 8 days of two model simulations: nudged to 50 km with (left) 1-h data and (right) free running.

Since atmospheric tides are characterized by very rapid variations in local time, their representation in nudged simulations is sensitive to both the time offset in the nudging process and to the temporal interpolation of the meteorological fields used for nudging. If tides were primarily responsible for the differences in the rate of error growth, we would expect that the differences would occur preferentially at zonal wavenumber 1 or 2, where the tidal amplitudes are largest, and that the differences in error growth between nudged and free-running simulations would be small in the stratosphere and lower mesosphere, where tidal amplitudes are small. Figure 4 indicates that the error in nudged simulations does increase rapidly for low wavenumbers but that the overall error growth over the broad range of wavenumbers is also large. Further investigation (not shown) indicates that the RMS error due to tides is relatively small compared to that from other large-scale features. The time scale for tidal forcing by time-varying heating is short (a few hours), compared to that of changing the temperature by the nudging process (~50 h). As a result, the day-to-day variations in the tidal amplitudes and phases are similar between the different nudged and free-running simulations.

The wavenumber breakdown of RMS error shown in Fig. 4 persists for the duration of the simulations. To get a picture of the distribution of error after the initial growth period, see Fig. 5, which shows a longitude-by-latitude cross section of the RMS error at 0.004 hPa averaged over 10 days for a simulation with nudging to 50 km. Both large- and small-scale features can be seen in the distribution of RMS error.

Fig. 5.

Longitude–by-latitude distribution of RMS error of zonal wind (m s−1) at 0.004 hPa from a simulation nudged to 50 km, averaged over the period 1–10 Feb.

Fig. 5.

Longitude–by-latitude distribution of RMS error of zonal wind (m s−1) at 0.004 hPa from a simulation nudged to 50 km, averaged over the period 1–10 Feb.

To further explore the role of infrequent meteorological data in contributing to the RMS error growth, we performed an additional simulation using nudging data available at every time step. The results (not shown) indicate no noticeable improvement over the simulations with data available at hourly intervals. From this test we conclude that the lack of higher temporal resolution of meteorological data is not the primary cause of the rapid error growth of nudged simulations.

This leaves us with the remaining potential explanation that the temporal offset that is inherent in the nudging process used in WACCM leads to an immediate offset between the nudged fields and the data used for nudging. Recall that the temporal offset as shown in Eq. (4) is one time step (30 min). One consequence of the offset is that increasing the value of α in Eq. (3) (i.e., making the nudging stronger) will not remove the offset. This was tested in several simulations that were nudged to 125 km with different values of α. The results (not shown) indicate that the offset between the nudged simulation and the meteorological fields used to nudge it did not approach zero, even for a relaxation time scale as short as 1 h. Based on this and the discussion above, we conclude that the rapid error growth in the early days of nudged simulations is in part a result of the process we use for nudging together with the fairly long time step of 30 min in the CESM models.

The simulations shown here illustrate the contribution of the nudging formulation to the initial error growth in the first week of WACCM simulations. This is not a practical concern for investigations using the specified dynamics version of the model since data from the spinup period are normally discarded. The present simulations cannot be used to determine what, if any, additional error is introduced to the later stages of nudged simulations; for this, an alternative method of nudging would be required.

b. Role of parameterized gravity wave drag

One well-accepted source of uncertainty in forcing the large-scale flow in the mesosphere is from small-scale gravity waves, which are the dominant subgrid-scale processes acting in the MLT, but which are poorly constrained by available observations. The dissipation and breaking of mesoscale gravity waves drive the strong circulation in the summer and winter hemispheres and contribute to other aspects of the circulation and dissipation of resolved waves. Current whole atmosphere models, including WACCM, cannot resolve most of these waves and therefore represent their impacts using parameterizations. The WACCM parameterizations are described by McFarlane (1987) for orographic waves, Garcia et al. (2007) for the general formulation of nonorographic waves, Beres et al. (2005) for convectively generated wave sources, and Richter et al. (2010) for frontally generated wave sources. The nonorographic gravity wave sources in WACCM4 depend on the resolved dynamics in the troposphere through the convection parameterization and frontal function. The momentum forcing in the MLT depends not only on the source distribution and characteristics but also on the temperature and winds through the atmospheric column, which affect wave propagation and dissipation.

The zonal and seasonal mean of the parameterized gravity wave drag is smooth in space and time, but this mean is made up of values that vary widely. The variations can be attributed to two features: the interactive source distributions, which vary with convective activity or fronts, and the propagation from the troposphere to the mesosphere, which depends on winds and temperature at all levels above the upper troposphere. To investigate the impact of the gravity wave parameterization on the RMS error, we repeat the set of simulations shown in Figs. 14 (see section 3a), but with different schemes for representing gravity wave drag. In the second set of runs, the nonorographic gravity wave source distribution from the parameterization in WACCM3 is used; this parameterization specifies a gravity wave source distribution that varies smoothly with latitude and season (Garcia et al. 2007) but is otherwise identical to the WACCM4 scheme. The third set of runs replaces the gravity wave scheme with Rayleigh friction. In the Rayleigh friction simulations, the momentum forcing of horizontal winds is represented by a damping of the form F = −kRU that is applied to the horizontal vector winds U. The coefficient kR has a value of zero in the troposphere and stratosphere and about 0.1 day−1 in the mesosphere (e.g., Leovy 1964); it is given by kR = C{1 + tanh[(z − 50)/10]}cos(ϕ), where C = 0.05, z is altitude (km), and ϕ is latitude. The gravity wave parameterization in WACCM computes not only momentum forcing but also eddy diffusion coefficients that are applied to temperature and trace gases. In the Rayleigh friction simulations, we use a fixed profile of eddy diffusion determined from the global average from the true simulation; the value is negligibly small in the troposphere and stratosphere and increases to about 100 m2 s−1 in the upper mesosphere.

As a result of the different representation of momentum forcing and eddy diffusion, the mean wind and temperature are somewhat different from the WACCM4 variations in the simulations that use the WACCM3 gravity wave scheme or Rayleigh friction. The values for temperature and zonal wind are shown in Fig. 6. The zonal winds for the simulations using WACCM3-specified gravity wave sources are quite similar to that using the WACCM4 interactive sources. The zonal wind in the simulation using Rayleigh friction is somewhat different but captures key features, such as the closure of the winter and summer jets.

Fig. 6.

Zonal-average (top) temperature (contour interval: 10 K) and (bottom) zonal wind (contour interval: 15 m s−1) for January using WACCM4 interactive gravity wave sources, WACCM3-specified gravity wave sources, and Rayleigh friction.

Fig. 6.

Zonal-average (top) temperature (contour interval: 10 K) and (bottom) zonal wind (contour interval: 15 m s−1) for January using WACCM4 interactive gravity wave sources, WACCM3-specified gravity wave sources, and Rayleigh friction.

With the WACCM4 gravity wave parameterization, the net monthly zonally averaged zonal momentum forcing from the sum of the three types of parameterized waves can range from about −200 to 200 m s−1 day−1. The monthly averages have contributions from individual time steps and grid points that are highly variable and have extremes ranging up to several thousands of meters per second per day. Figure 7 shows the probability of occurrence of zonal momentum forcing values at individual grid points in the upper mesosphere for the first week of each base case; that is, this is the likelihood that a particular range of momentum forcing values will be seen for a given grid point and time step.

Fig. 7.

Probability of occurrence of a given value of gravity wave zonal momentum forcing at 0.004 hPa (~85 km) at an individual grid point and time step during January from the WACCM gravity wave parameterization with interactive sources (black), the parameterization with specified sources (red), and Rayleigh friction (blue asterisks).

Fig. 7.

Probability of occurrence of a given value of gravity wave zonal momentum forcing at 0.004 hPa (~85 km) at an individual grid point and time step during January from the WACCM gravity wave parameterization with interactive sources (black), the parameterization with specified sources (red), and Rayleigh friction (blue asterisks).

The most commonly seen probability from the parameterization with interactive gravity wave sources is zero; this occurs at about 68% of the total grid points/time steps. Drag values of exactly zero occur when both 1) meteorological conditions at a grid point do not reach the threshold for frontal or convective wave generation and 2) orographic gravity waves are not generated or are absorbed at a critical line below this altitude. For nonzero drag, the probability of occurrence is highest for low drag magnitudes of under a few hundreds of meters per second per day and becomes increasingly small with larger positive and negative drag. Magnitudes as large as ±5000 m s−1 day−1 (sum of all source types and all phase speeds in the gravity wave spectrum) have a nonzero occurrence rate but are extremely rare.

The distributions for the sum of gravity wave momentum forcing for the other two gravity wave schemes are also shown on Fig. 7. When the sources are specified, the range of values seen is much narrower, and the probability of a drag value that is identically zero is much smaller. The tails of the probability distribution are qualitatively different from those using the WACCM4 gravity wave sources. When the parameterization is replaced with Rayleigh friction, all the drag values are between −100 and 100 m s−1 day−1.

Figure 8 shows the global RMS error at 0.004 hPa (~85 km) for simulations with the WACCM3 and Rayleigh friction representations of gravity wave drag, for comparison with Fig. 1. It is clear that the different gravity wave drag schemes lead to large differences in the rate of RMS error growth and in the error levels that are reached after 40 days. The rate of divergence between the base case and the free-running simulations (black lines on Figs. 1 and 8) is slower than with the standard model, although the RMS errors eventually plateau at a similar value. All simulations show the faster error growth of nudged simulations during the early days of the simulations, as originally noted for the standard WACCM4 (Fig. 1). The RMS errors for nudged simulations (other colors) that are eventually reached are substantially smaller in simulations that do not include the gravity wave parameterization using interactive sources; the simulations using WACCM3 gravity wave sources are intermediate between the WACCM4 settings (Fig. 1) and Rayleigh friction (right panels of Fig. 8). The most striking difference in these simulations is the strong drop in RMS error for the nudged simulations without the gravity wave parameterization using interactive sources, even when the nudging is used only in the troposphere and stratosphere.

Fig. 8.

As in Fig. 1, but for simulations with (left) fixed gravity wave sources and (right) gravity wave parameterization replaced by Rayleigh friction. All nudged cases use meteorological data every hour. Nudging to 125 km is not shown.

Fig. 8.

As in Fig. 1, but for simulations with (left) fixed gravity wave sources and (right) gravity wave parameterization replaced by Rayleigh friction. All nudged cases use meteorological data every hour. Nudging to 125 km is not shown.

Figure 9 shows a direct comparison of the RMS errors from the three different schemes for gravity wave drag. The nudged simulations clearly show that the highest errors occur with interactive gravity wave sources; using the same gravity wave parameterization with specified wave sources reduces the error; and using Rayleigh friction in place of the parameterization reduce it even further. The same pattern can be seen for errors in the winter high latitudes (Fig. 10). In contrast, the RMS errors for the free-running simulations do not show systematic dependence on the scheme used for representing gravity waves.

Fig. 9.

Global RMS error for three different representations of gravity wave drag: interactive sources (solid), specified sources (dashed), and Rayleigh friction (dotted). Red lines indicate errors for simulations nudged to 50 km; black lines indicate RMS differences for free-running simulations.

Fig. 9.

Global RMS error for three different representations of gravity wave drag: interactive sources (solid), specified sources (dashed), and Rayleigh friction (dotted). Red lines indicate errors for simulations nudged to 50 km; black lines indicate RMS differences for free-running simulations.

Fig. 10.

As in Fig. 9, but for the Northern Hemisphere poleward of 70°N.

Fig. 10.

As in Fig. 9, but for the Northern Hemisphere poleward of 70°N.

The reason for the reduced RMS error of the nudged cases when the parameterized gravity wave drag sources are specified rather than determined interactively and the further reduction when the parameterized drag is replaced by Rayleigh friction is straightforward. As seen in Fig. 7, the gravity wave drag using the WACCM4 parameterization with interactive sources can be quite large at individual grid points and can vary quite rapidly from one grid point to the next and from one model time step to the next. The sources of the gravity waves depend on a frontogenesis function (Richter et al. 2010) and convective parameterization (Beres et al. 2005); the net drag in the MLT is also sensitive to the horizontal winds throughout the atmospheric column above the sources. The parameterization is deterministic, in the sense that the model can be run multiple times and, as long as no other perturbations are introduced, the gravity wave forcing will be identical. However, even a small change in the source distribution or propagation conditions can have a large impact on the column forcing at a particular grid point and time step. One impact of the parameterization is therefore to amplify small changes. This may be a realistic representation of the atmospheric impact of gravity waves.

When the sources are specified, the range of momentum forcing values is much narrower, as seen in Fig. 7. There is still substantial variability caused by variations in the propagation of the parameterized gravity waves, which depends on the winds and temperature of the atmosphere in a column above the source. Removal of the variability from interactive wave sources leads to a more predictable MLT but may also lead to an underestimate of the error growth in simulations of the mesosphere using nudging of the troposphere and stratosphere.

The overall picture that emerges is that, when the model has more degrees of freedom, the MLT dynamics cannot be predicted based on good but not perfect knowledge of the tropospheric dynamics. Realistic representation of model error has important implications for assimilation of MLT data into whole atmosphere models (e.g., Pedatella et al. 2014b) and is a central step in ensemble prediction for climate projection and weather forecasting (e.g., Berner et al. 2012; 2009). As shown here, a leading source of model error in the MLT is due to poor constraints on gravity wave forcing from the troposphere. The neglect of the model error due to inadequate gravity wave drag parameterization by, for example, using specified rather than interactive sources, leads to an unrealistic representation of the model uncertainty in ensemble data assimilation and forecasting systems and therefore to poor assimilation analysis and forecast results.

The role of gravity waves is supported by the longitude–latitude error distribution shown in Fig. 5. A swath of high error can be seen in the southern middle and high latitudes associated with gravity wave sources in the storm tracks. In the Northern Hemisphere, there are planetary-scale variations of the error that are consistent with large-scale variations in the ability of gravity waves to propagate due to filtering by winds from middle-atmosphere planetary waves. Higher error is also seen over the Indonesian region, where convective activity is vigorous.

We cannot fully validate the WACCM gravity wave parameterization since there is not a version of the model with the high horizontal, vertical, and temporal resolution that would be needed to simulate the full spectrum of gravity waves and their interaction with the background atmosphere, nor are there sufficient observations of the wave momentum forcing in the mesosphere. The parameterization has been tuned so that the magnitude of the zonal- and time-mean momentum forcing gives a realistic circulation and thermal structure. It is possible that, because of the relatively coarse horizontal (about 2°) and temporal (30 min) resolution, the parameterized gravity waves at each grid point have a more forceful impact than is realistic. If this is the case, then the WACCM simulations shown here could have exaggerated the increase in RMS error due to gravity waves. Even if this is the case, the comparison of simulations with the three model versions gives evidence that much of the unpredictability of the MLT region derives from the repeated forcing by gravity waves that are generated by tropospheric convective and frontal events and that have large momentum flux divergence over small spatial and temporal ranges. Even with nudging, there are small uncertainties in these tropospheric processes that amplify as they propagate to the MLT.

4. Conclusions

The primary goal of the model experiments presented here is to assess the predictability of the MLT when complete information about the lower atmosphere and the external forcing is available. The combined results from 24 model simulations show a limitation to the ability to predict the MLT. The leading cause is the inability to constrain perturbations in the MLT driven by dissipating gravity waves. The gravity wave sources in the troposphere and their propagation through the atmospheric column are sensitive to small variations in the background atmosphere; these variations then amplify and have a large impact on the MLT dynamical fields.

The tools used for this investigation are nudged and free-running simulations of WACCM. The nudging process in WACCM constrains the large-scale dynamical fields in a portion of the atmosphere from Earth’s surface to a specified level in the middle atmosphere. Above the nudging region, the model is free running. To set up these experiments, we save hourly output from a free-running simulation and use it to nudge the later simulations. With this configuration, we know the exact global fields that the nudged model is meant to simulate. We can compute errors and investigate the impact of different aspects of the nudging on the simulation.

The nudged simulations begin to diverge from the base case immediately and reach a stable range of RMS error after about 30 days. The RMS errors increase with height and are lower when the nudging extends to higher altitudes. The errors are also lower when meteorological data are available at the shorter time interval of 1 h rather than the standard 6 h. Cases where the nudging is applied only to the troposphere or to the troposphere and stratosphere show substantial RMS errors but do have some improvement over the divergence in free-running simulations. RMS errors of the daily zonally averaged fields are lower than those calculated from the individual grid points and time steps.

Different representations of the gravity wave drag are used to investigate the role of the parameterized gravity waves in contributing to the errors. The momentum forcing from the standard WACCM4 parameterization can have very large drag values that are seen only intermittently. In WACCM4, the sources of nonorographic gravity waves are determined interactively and change as the details of tropospheric dynamics change. When the gravity wave parameterization is replaced by a linear damping, nudging of the troposphere alone leads to a strong reduction of the RMS error compared to the simulations with gravity wave parameterization included or to free-running simulations either with or without a gravity wave parameterization. This indicates that the nudging process is able to remove the bulk of the variability that leads simulations in the upper levels to diverge but that the process cannot remove the large additional variability that ultimately results from interactive gravity wave sources. Observations indicate that gravity wave momentum flux magnitudes in the atmosphere also are intermittent and strongly varying (e.g., Hertzog et al. 2012), so the RMS errors of constrained simulations presented here may be qualitatively realistic.

The present simulations show that the inherent limitations to observing or predicting gravity wave generation in the troposphere (Doyle et al. 2011) contribute to the uncertainty of the MLT through variations in the sources of gravity waves and their amplified impact on the MLT. This uncertainty in the sources persists and is an important error source in the MLT, even when the tropospheric horizontal winds and temperatures are nudged to the “true” conditions. With these model experiments, we cannot evaluate the possible improvements that could be gained in the MLT error growth if the gravity wave sources were more realistic. For this we would need further validation of the source determinations from high-resolution observations.

Although the error growth in WACCM is larger with a model that includes a more complex representation of gravity wave drag, this should not be interpreted to indicate that a simpler model would give a more realistic simulation of the MLT. Rather, it is an indication that the added error growth is directly related to the complexity of the model. The parameterization representing gravity wave generation and propagation was put into the model to represent actual physical processes in the atmosphere. The process by which the lower atmosphere and middle atmosphere affect the MLT leads to error growth that weakens the control of the upper-atmosphere dynamics by the large-scale processes in the lower atmosphere and leads to unpredictability.

Using WACCM3, Liu et al. (2009) found that constraining the troposphere by frequent reinitialization could reduce error growth in the mesosphere. A subset of simulations presented here uses the WACCM4 gravity wave parameterization but with specified wave sources; these simulations therefore have a representation of gravity waves that is equivalent to that in WACCM3. Our results are not completely consistent with those of Liu et al. (2009) since, in the present simulations, nudging the troposphere is not sufficient to strongly reduce error growth in the middle and upper atmosphere.

A number of studies have used specified dynamics WACCM and other nudged high-top models to investigate processes in the atmosphere above the top of the nudged region. In these cases, the fields used for nudging are derived from assimilated atmospheric observations. Some success is seen, for example, in simulations to investigate the MLT response to stratospheric sudden warmings (e.g., Tweedy et al. 2013; Chandran and Collins 2014; Pedatella et al. 2014a; Stray et al. 2015). The discrepancies between the simulations and the analyses used to nudge them have contributions from net biases between the model and observational analyses. The present study indicates that some discrepancies will persist even if the biases between the meteorological analyses and model climatology are reduced.

Acknowledgments

We thank Jérôme Barré and Álvaro de la Cámara for helpful comments on an earlier version of this paper. WACCM is a component of the Community Earth System Model (CESM), which is supported by the National Science Foundation (NSF) and the Office of Science of the U.S. Department of Energy. CESM and the files needed to run it are available from NCAR (see http://www.cesm.ucar.edu/models/register/register.html for registration). Computing resources were provided by NCAR’s Computational and Information Systems Laboratory (CISL). The setup and output from the simulations in this study are available from the lead author. AKS acknowledges support from NASA Award NNX14AD83G, and TM acknowledges support from NASA Award NNX14AI17G.

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Footnotes

a

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