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Canadian Middle Atmosphere Model

Description

Only a brief description of the relevant features of the CMAM are outlined here. For a general description refer to Beagley et al [1997]. The version of the model discussed herein has a T32 spectral resolution and 50 levels in the vertical. This corresponds to a horizontal resolution of approximately 5$^{\circ}$ and a vertical resolution which varies from less than one kilometer in the troposphere to about 3-4 km in the stratosphere and mesosphere. The upper boundary of the model is located at about 97 km. One physical parameterization in the troposphere which plays a crucial role in determining the ease with which a middle atmosphere GCM generates long period mean wind oscillations in the tropical stratosphere is the convection scheme. In the CMAM the deep convective parameterization of Zhang and McFarlane [1995] is used.

The effects of unresolved gravity waves are parameterized using the Doppler spread parameterization. The DSP requires the specification of the vertical wavenumber ($m$) spectrum of horizontal winds at the source level which is taken to be the ground. For simplicity and convenience a wavenumber spectrum that is proportional to $m$, with a minimum allowable wavenumber of 1/(3km), is employed. The momentum flux source is assumed to be horizontally isotropic and independent of time and longitude. More details of the scheme and its impact on the CMAM can be found in McLandress [1998].

Results

The remainder of this presentation focusses mainly on results from two 6-year simulations of the CMAM. The first is one in which the source level rms horizontal winds ($\sigma^2$) of the DSP are set to the uniform value of 1.5 m$^2$/s$^2$. The second simulation is one in which $\sigma^2$ is enhanced at low latitudes, i.e., $\sigma^2(\theta)=1.5+\mbox{e}^{-(\theta/15^{\circ})^2}$. Timeseries of the zonal mean winds at 10 mb (as a function of latitude) and at 3$^{\circ}$N (as a function of height) are shown in Figures 3 and 4, respectively, for the two experiments. The simulation using the uniform rms winds exhibits a strong semi-annual variation in the upper stratosphere and mesosphere but no obvious signs of a longer period oscillation in the lower stratosphere. However, in the presence of the enhanced gravity wave momentum flux in the tropics, an oscillation with a period of approximately 18 months appears. Unlike the observed QBO, this oscillation appears to be phase locked to the annual cycle as seen in the right panel of Figure 3. Synchronization with the seasonal cycle has been observed in other numerical simulations of the QBO using large gravity wave fluxes [Dunkerton, 1997].

\includegraphics[width=0.48\textwidth]{ubar_10mb_ym5fc.epsi}

\includegraphics[width=0.48\textwidth]{ubar_10mb_ym5ff.epsi}

Figure 3: Timeseries of the monthly average zonal mean zonal wind at 10 mb (32 km) from CMAM for the simulation using the uniform gravity wave source (left) and equatorially enhanced gravity wave source (right). Contour interval is 10 m/s.

\includegraphics[width=0.48\textwidth]{ubar_3n_ym5fc.epsi}

\includegraphics[width=0.48\textwidth]{ubar_3n_ym5ff.epsi}

Figure 4: Timeseries of the monthly average zonal mean zonal wind at 3$\,^{\circ }$N from CMAM for the simulation using the uniform gravity wave source (left) and the equatorially enhanced gravity wave source (right). Contour interval is 20 m/s.

 

Role of Resolved Waves

The role of the resolved waves in driving the oscillation is of obvious importance. Figure 5 shows profiles of the mean winds, Eliassen-Palm flux divergence (EPFD), and gravity wave momentum flux divergence (GWD) at two different phases of the oscillation separated by approximately one-half of a period. The dotted curve, which shows the EPFD computed using only zonal wavenumbers 1-10, indicates that the bulk of the resolved wave driving (at least using this relatively coarse temporal sampling) arises from the large-scale components of the flow. GWD is seen to be the dominant term, which is not surprising since the deep convective parameterization of Zhang and McFarlane [1995] is known to produce a very red latent heating frequency spectrum, which results in relatively weak momentum fluxes in the lower stratosphere by the resolved waves.

\includegraphics[width=0.7\textwidth]{u_gwepfd_ym5gf_mono.epsi}

Figure 5: Zonal mean zonal wind (thick solid), gravity wave drag (thin solid), Eliassen-Palm flux divergence for all zonal wavenumbers $k$ (dashed) and for $k=1-10$ (dotted) at 3$\,^{\circ }$N for July year 3 (left) and April year 4 (right) from CMAM for the simulation using the equatorially enhanced gravity wave source.

Finite Difference Considerations

The final set of results which are shown in Figure 6 demonstrate the impact of the form of the finite difference equation used to evaluate the parameterized gravity wave flux divergence. Here, one-sided differences are used in contrast to the centered differences employed in all of the previous results. In the left panel the GWD at level $l$ is computed by differencing the flux at the level above ($l+1$) and the flux at level $l$, while in the right panel fluxes at levels $l$ and $l-1$ are used. In both cases the background density appearing in the denominator is evaluated at level $l$. (The latter form is believed to be currently used in several middle atmosphere GCMs which employ the DSP.) The resulting impact on the oscillation is rather large. Thus, some care must be taken in attributing the period and amplitude of the simulated oscillation to only the magnitude of the parameterized momentum flux at the source level since different finite difference schemes can produce very different results.

\includegraphics[width=0.48\textwidth]{ubar_3n_ym5gi.epsi}

\includegraphics[width=0.48\textwidth]{ubar_3n_ym5gj.epsi}

Figure 6: Timeseries of the monthly average zonal mean zonal wind at 3$\,^{\circ }$N from CMAM for the simulation using the equatorially enhanced gravity wave source and one-sided finite differences from below (left) and from above (right). Contour interval is 20 m/s.

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