On the use of a simple two-level model in general circulation studies

Numerical experiments with a two-level, quasi-geostrophic model, described by Davies and Davies (1969), have been extended in several ways; the grid spacing of the previous model has been halved, greatly reducing numerical errors, and the lateral East-West span of the flow domain is much increased. Using this model a preliminary study is made of some of the large-scale features of the dynamics of baroclinic wave blocking by the formation of cold anticyclonic cells in high latitudes. In order to facilitate the computational work and the interpretation of the numerical results, a simple, idealized distribution of the large-scale thermal characteristics of an ocean and a continental region is chosen. Two variants of the model are compared : model (a) is based on a heating function (independent of longitude) describing the climatological annual average over ocean surfaces : in model (b) the flow domain is divided into two longitudinal (North-South) zones; heating functions, roughly characteristic of annual and winter averages over the ocean surfaces, are used over one zone and heating functions, roughly characteristic of similar averages over land surfaces, are employed over the other zone. Time integrations for the models have been carried out for periods of 110 days. Blocking does not take place in model (a) but in model (b) the computed flow charts and the K′ (t) function (total model eddy kinetic energy) lead to the interesting result that ‘blocking’ takes place in high latitudes of the ‘land mass’ area at broad scale minima of K′, strongly suggesting that the blocking phenomenon is associated with global scale parameters. In the model those minima of K′ associated with a large-scale, longitudinal, land-sea temperature differential of about 2°C led to blocking, but the minima associated with temperature differentials appreciably less than this did not produce blocking. The results also indicate an approximately linear dependence of the time scale of blocking on the large-scale, longitudinal, land-sea heating function differential. The prediction that blocking is associated with broad scale minima of K′ has been studied in an analysis of Northern Hemisphere synoptic charts for the winter of 1956–57, which include a well-formed blocking situation. Estimates of eddy kinetic energy were made for both surface and 500 mb charts for the sections (a) between 50°W and 60°E, (b) between 110°W and 120°E, and for (c) the whole Northern Hemisphere. In each of these cases K′ dropped to a well marked minimum just before the incidence of a characteristic blocking situation over north-west Europe from 21 December to 28 December, the behaviour of K′ (t) over this period being closely analogous to that found in the model blocking situations. Another objective of the study is to make a comparison of two formulations of sub-grid scale representation. In the first instance, this is taken in the often-used form A°2 u, where u is the appropriate velocity component and A is an invariant of space and time; in the second case A is linked to model values of grid-scale temperature gradient. A comparison indicates a much higher (and therefore more realistic) degree of variability of flow pattern leading to a 50 per cent higher value for the computed ratio of eddy to zonal kinetic energy.