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ABSTRACT
The linear theory of point correlation maps for synoptic systems relies so far mainly on specifications of stochastic forcing due to nonlinear processes that are not based on observations. Forty-year ECMWF Re-Analysis (ERA-40) data are used to derive time series of the forcing terms in a potential vorticity equation for a correlation point in the North Atlantic storm-track region. It is found that the forcing correlations are restricted to distances less than 1500 km to the correlation point in zonal direction and just a few hundred kilometers in meridional direction. The forcing is not even approximately white in time. Covariances of forcing and potential vorticity are presented as well. An advection equation with simple damping and realistic stochastic forcing is solved to approximate the observed covariances of forcing and potential vorticity.
(ProQuest: ... denotes formulae omitted.)
1. Introduction
By now, the statistical features of extratropical weather systems have been explored in some detail (e.g., Hoskins and Hodges 2002, and references therein). We are informed about the location of the stormtracks, the related transports of momentum and heat, and the changes of eddy statistics with lag. As demonstrated by Blackmon et al. (1984) and many others, the correlations of heights at a reference point and all other points form a wave pattern at lag τ = 0 with decay of the wave amplitudes upstream and downstream. This pattern is normally moving eastward, intensifies with increasing negative lag, and becomes weaker for positive increasing lag. An example is presented in Fig. 1 where potential vorticity (PV)
... (1.1)
is selected as a variable with density ρ, vorticity ζ, potential temperature θ, and Coriolis parameter f. The data evaluation is based on the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re- Analysis (ERA-40) data (see section 2). Although q is not strictly conserved in adiabatic and frictionless flow, the deviations of q from the correct formulation in isentropic coordinates are too small to be of interest here. Let us denote by C(b, c|τ) the covariance of variable b and variable c where b leads with lag τ. Figure 1 shows the regression ... at the correlation point (dot in Fig. 1) and PV at all other points at the constant height surface z = 8...