To summarise our results, changes to the stratospheric potential vorticity have a significant impact on the development of baroclinic instability in an Eady-like model. The dependence is such that increasing the strength of the polar vortex tends to decrease the eddy growth in the troposphere. This is found not just in the zonally symmetric cases, comparing zonally symmetric stratospheric pertur- bations of different potential vorticity magnitudes, but also in cases of zonally asymmetric disturbances to a polar vortex of given potential vorticity. The lat- ter scenario extends previous work that has considered only zonally symmetric stratospheric perturbations. In particular, we found that there is a large dif- ference in the tropospheric evolution between cases representing a strong vortex and cases representing the vortex following either a wave-one or wave-two sudden warming. Differences in the tropospheric evolution include the growth of eddy kinetic energy and wave activity, as well as synoptic scale details of the wave breaking and the latitudinal extent of mixing within the troposphere.
Our study differs fundamentally in philosophy from the related work of Wittman
et al.(2004, 2007) in which perturbations were made to the stratospheric zonal winds. It is of course true that by perturbing the stratospheric potential vortic- ity, as is done here, one is also perturbing the tropospheric zonal flow. However, because of the fundamental nature of the potential vorticity (e.g. Hoskinset al., 1985) it is perhaps justified to consider such stratospheric potential vorticity perturbations as dynamical perturbations to the stratosphere only. In our case, these perturbations have been carefully isolated from the troposphere by includ-
ing a “subvortex” region between the troposphere and lowermost polar vortex in which the potential vorticity is unperturbed. Moreover, actual differences in the initial tropospheric zonal winds between zonally symmetric and asymmetric perturbation cases are very slight (compare Figure 3.1(b-d)). Finally, this kind of perturbation is arguably closer to the situation resulting from a stratospheric sudden warming. One of the important results of the present work is that the po- tential vorticity perturbations made here result in significantly larger differences to the tropospheric evolution than obtained by perturbations to the stratospheric winds alone.
One significant difference between our results and those of Wittman et al. is the sense in which a stratospheric perturbation affects the growth of the insta- bility. Wittman et al. found an increase in eddy growth rates with increasing stratospheric shear, whereas we find a decrease in growth rates with increas- ing stratospheric potential vorticity. The results are not inconsistent when full account is taken of changes to the tropospheric shear resulting from the strato- spheric potential vorticity perturbation in our case, which tends to leave the ver- tical shear unchanged but increases the horizontal shear. The decrease in growth rates we observed may therefore be attributed to a change in the nature of the baroclinic development similar to that found by Thorncroft et al. (1993). One conclusion that may be drawn from both Wittman et al. and the present work is that the tropospheric evolution depends rather sensitively on the stratospheric state through details of the shear in the troposphere and near the subtropical jet.
Chapter 4
An Online Trajectory Model
Before proceeding further with a detailed analysis of mixing and transport in another context we introduce a tool which will be used to investigate the effect of the quasi-biennial oscillation on transport and mixing in the stratosphere. Examining lateral mixing and transport in the stratosphere requires us to be able to follow Lagrangian particles and thus motivates the use of a trajectory model.
The trajectory model we use is based on the “Offline” trajectory code written by John Methven at Reading University in 1997 (Methven, 1997). We have modified and developed this code to ensure compatibility and integration within the unified model (UM), the general circulation model that is developed and used at the UK Met Office. These developments allow trajectories to be calculated with greater accuracy.
4.1
Offline trajectory code
The “offline” trajectory code calculates trajectories from ECMWF data or data output from the University of Reading’s spectral model. The term “offline”
denotes that the input data, comprising the advecting wind fields, has been out- put from a model. The trajectory calculations involve solving the first order ordinary differential equation
dx
dt =u(x, t) (4.1)
where x is a particles position in space, u is the four dimensional wind field (space and time) and t denotes time. A brief outline of how the code works is displayed in Figure 4.1. The particles can be initialised in a variety of ways: on a specific model level or levels, on pressure surfaces, or on isentropic surfaces. The distribution of the particles in longitude and latitude can also be varied allowing them to be initialised in a region of particular interest.
Wind records from ECMWF are typically six hourly, twelve hourly or daily. The time interval between wind records is divided into N subintervals, where typicallyN = 10, to give a constant integrator timestep,δt. The four dimensional wind records,(x,y,z,t), are interpolated to the current particle positions in space and time. Then a fourth order Runge-Kutta numerical integration method is used to advect the particles over the integrator timestep δt. This process is repeated until the particles have been advected to the time of the second wind record.
As well as advecting particles the “offline” trajectory code can assign the values of meteorological fields such as temperature, potential vorticity and water vapour as attributes to the particles. The values of these fields are interpolated to each particles position at each timestep. Being able to assign attributes to parti- cles is a very useful tool which can be used to diagnose possible non-conservative forces, to diagnose the minimum temperature encountered along a trajectory (im- portant for setting the water vapour concentrations) and also to trace a specific group of particles, for example those that started within the polar vortex.
The wind records and attribute fields are read.
Position the particles you wish to advect.
The position of each particle is integrated between the 2 wind records. The next wind record
is read.
to the particles. Attributes are assigned
Particle positions and attributes are output.
Repeat until
trajectories
reach the
desired
length
cel trajectories in the sense that we track the path of a point in the flow by integrating (4.1). An air parcel can be thought of as a finite volume of air with certain characteristics. In a chaotic flow, any volume no matter how small will be stretched and ultimately folded. Therefore in a chaotic flow an air parcel has a finite existence whereas a particle trajectory can exist indefinitely.
A limitation of the “offline” trajectory code is in calculating full Lagrangian means which are sensitive to the sampling frequency. The normal six hourly sampling frequency of the “offline” trajectory code results in small scale motions, such as the up and down wave motion within the tropical stratosphere, being missed leading to inaccurate vertical velocities.