Past exam of the atmospheric physics course of the University of Cambridge / 2013 / Paper 1 / 3

A teleconnection is correlated atmospheric variability between separated regions. A principal dynamical pathway is a Rossby-wave teleconnection: a displaced air column conserves potential vorticity, so changing planetary vorticity must be balanced by changing relative vorticity. The background potential-vorticity gradient supplies the restoring mechanism.

In a uniform zonal current $U$ on a beta plane, a simple Barotropic Rossby wave hasThe intrinsic phase propagates westward for $\beta >0$; advection can leave a nearly stationary pattern in the terrestrial frame. Energy and information travel with the group velocity, not necessarily with individual crests or the same air parcels. A jet stream can guide wave packets and link distant ridges and troughs.

For example, persistent anomalous tropical heating can excite wave trains that alter remote pressure, temperature and storm tracks. Tropical Pacific ocean-temperature anomalies can modify that heating, yielding reproducible extratropical patterns. Their phase and strength depend on the background winds, potential-vorticity gradients, damping, season and eddy feedbacks. A correlation pattern is not by itself proof of a unique causal pathway, and not every teleconnection is a single stationary linear wave.^[ref]

A foehn wind is relatively warm, dry downslope air on a mountain's lee side. In the classical condensation pathway, ascending windward air expands and cools at the dry adiabatic lapse rate until the lifting condensation level. Condensation then releases latent heat, reducing the cooling rate to the moist adiabatic lapse rate. Atmospheric precipitation removes condensate, and the descending parcel warms by compression at approximately the dry rate. Its relative humidity falls.

For equal starting and finishing heights, complete condensate removal and a constant moist lapse rate above condensation height $z_c$, the precipitation-driven foehn warming isHere $H>z_c$ is the parcel's maximum height and ${\Gamma }_d>{\Gamma }_m$. The warming is adiabatic compression during descent, not heating by friction. Without condensation or a difference in source air, a reversible dry parcel returning to its original height would regain its original temperature.

Precipitation is not essential to every foehn event. Isentropic foehn drawdown can bring air of higher potential temperature from aloft down the lee slope; turbulent mixing and extra solar heating beneath clear skies can also contribute. The sketch shows the classical rainout pathway rather than asserting a unique mechanism.^[ref]

For dry atmospheric Ertel potential vorticity, use absolute vorticity ${\mathbf{\omega }}_a=\nabla \times \mathbf{u}+2\mathbf{\Omega }$ and potential temperature $\theta =T(p_0/p{)}^{R_d/c_p}$:The conservation statement is Ertel's theorem for smooth, inviscid, adiabatic flow with conservative body forces and a thermodynamic equation of state $p=p(\rho ,\theta )$. Stretching of ${\mathbf{\omega }}_a/\rho$ cancels deformation of $\nabla \theta$ in their material derivative; the remaining baroclinic triple product vanishes because $\nabla p$ lies in the span of $\nabla \rho ,\nabla \theta$. The atmospheric form includes $1/\rho$; the commonly used Boussinesq approximation version has a different normalization.

In a predominantly vertical stratification, $q_E\simeq (f+\zeta ){\partial }_z\theta /\rho$. Thus rotation and stratification jointly label air masses. Material conservation explains how parcels deform and stretch while preserving a useful scalar, supports Rossby waves, and helps diagnose sharp fronts, jets and stratospheric intrusions.

Under an appropriate balance model, potential-vorticity inversion recovers associated wind and temperature fields from a PV distribution together with stratification and boundary data. PV alone does not specify every component of an arbitrary atmospheric flow. Potential-vorticity generation by heating and friction limits conservative parcel reasoning near strong heating, surface stress or mixing.^[ref]