A mid-latitude Sea Surface Temperature Anomaly (SSTA) is introduced into a 9-level polar stereographic southern hemisphere model. Two 50-day anomaly integrations (SSTAR1 and SSTAR2) are compared with their respective control integrations. In SSTAR2 the anomaly is introduced 10 days later than in SSTAR1. Comparison of the two integrations reveals systematic effects in some regions of the Antarctic trough and the mid-Atlantic and Indian Oceans, but no systematic effect in the immediate area of the SSTA. The latter region shows a weak variation in SSTAR2 while SSTAR 1 is characterized by a strong variation and a blocking sequence some 20 days into the integration. The region of enhanced cyclogenesis in SSTAR1 occurs on the equatorial side of the anomaly and not the region of enhanced surface baroclinicity. One such large cyclone is a major feature of the blocking sequence. Enhanced latent heat release appears to be an important factor in these developments.

The effect of a warm mid‐latitude sea surface temperature anomaly on a numerical simulation of the general circulation of the southern hemisphere

A two-level, quasi-geostrophic, β-plane, general circulation model is developed, incorporating a time-dependent surface energy balance equation and a time-dependent heating function at the 500 mb level, with an associated feedback relationship. This system enables the surface temperature distribution to be evaluated as a function of time in the model, and so allows an associated variable spatial distribution of surface albedo to be carried in the model, including a simulated “snow and ice” edge. The effect on the model of successive small changes in solar radiation (of 1/2% up to a total of 3%) are then studied by carrying out numerical experiments over long time periods, these being sufficiently long (involving a total time of integration of 1800 model days) to produce oscillations in model heating and albedo distributions about asymptotic mean values. The successive latitudinal positions of the, zonally averaged, “snow and ice” edge agree approximately with those calculated by Gordon and Davies (1974) using a modified form of the statical energy balance method of Budyko (1969). However, the experiments also showed that the greater the reduction made in solar radiation the greater was the ensuing amplitude of spatial movement of the associated albedo distribution, implying a strong tendency towards instability of the simulated edge as the reduction approached a value of 3%. DOI: 10.1111/j.2153-3490.1977.tb00761.x

The sensitivity of response of climatic characteristics in a two-level general circulation model to small changes in solar radiation

The Behaviour of the Stationary and Travelling Planetary-Scale Waves during Blocking - A Northern Hemisphere Data Study

The great philippine floods of 1972

The development of turbulence is studied numerically through the use of a simplified two-level quasi-geostrophic model. The domain occupied by the fluid has 64 times 64 grid points in the horizontal and obeys cyclic boundary conditions in the x - and y -directions. The turbulence is generated by a heating function composed of the 2-dimensional fourier components having the larger wave number, m = 8. Three cases are investigated for two values of H , the amplitude of the heating function and two values of v , the coefficient of eddy viscosity. Quasistationary spectra are obtained in each case. The slopes of the spectra for 8 ? m ? 16 on a log-log graph vary from ?1.7 to ?3.4 depending on v and H . The nonlinear cascade of available potential energy is found to be toward larger wavenumbers. The nonlinear cascade of kinetic energy is from components for which 8 ? m ? 14, mainly toward 1 ? m ? 7, the larger scales. The gains for m > 14 resulting from the cascade is relatively small. These transfers are in qualitative agreement with atmospheric observations. Gains of enstrophy are observed to be fairly constant for 14 ? m ? 28. In an inertial subrange they should be zero. Relatively small gains are recorded for m < 7 while the spectral region 8 ? m ? 14 acts as source. Except for the wavenumber of transition from negative to positive values the distribution of losses and gains of enstrophy due to the inertial cascade is similar to that resulting from calculations based on atmospheric observations. It is concluded that the two dimensional turbulence theories enunciated by Fjortoft, Kraichnan and Leith pertain to the model in this study and the atmosphere (so far as our model resembles the atmosphere) in the prediction of the dominant direction of the nonlinear cascades of kinetic energy and enstrophy in wavenumber space. Inertial subranges in which the cascades result in zero changes are neither observed in the numerical experiments of this study nor in calculations based on atmospheric observations in the spectral region 8 ? m ? 16. The experiments described in this paper were performed prior to the theory proposed by Charney and so were not designed to be a test of it. However, some assumptions and conclusions are discussed in the light of that theory. DOI: 10.1111/j.2153-3490.1973.tb00607.x

Numerical simulation of quasi-geostrophic turbulence

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.

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

A representation of an ‘Ekman’ type of boundary layer (assumed to extend from 1,000 mb to 900 mb) is inserted into a two-level, quasi-geostrophic, general circulation numerical model. An approximate time-dependent analytic solution of this boundary layer is matched to the ‘free atmosphere’ regime of the model through the vertical velocities produced at the grid points. By using this analytic solution the essential physical characteristic of the observed continuous increase with height of scale length of turbulence in the boundary layer is represented. By comparing time integrations of two models, only one of which contains an Ekman layer, it is shown that large-scale flow characteristics, expressed in terms of growth rate of zonal and eddy kinetic energy, are sensitively dependent on the presence of such a layer in a numerical model.

Ekman boundary layer interactions in a numerical model of the general circulation

A two-level, quasi-geostrophic model, described by Everson and Davies (1970), is used to study the dependence of duration of predictability (as defined by, e.g., Charney et al. 1966) on the phase, at some initial time in the integration, of global scale baroclinic development (expressed in the model in terms of fluctuations in eddy kinetic energy, K').

Using firstly an invariable subgrid scale coefficient in a control run of 120 days, sinusoidal perturbations, wave length approximately 6,000 km, of the geopotential heights are inserted at all the grid points at (a) day 72, corresponding to a maximum in model K', and (b) day 84, corresponding to a minimum in model K'. The consequent ‘perturbed’ integrations are compared to the control values by taking the r.m.s. of the difference in the 500 mb calculated temperature distributions, and determining the time taken for this to increase to the ‘persistence’ value, i.e. the maximum r.m.s. difference between two randomly selected model states. The doubling time of error in (a) was seen to be 12 days leading to a model predictability of 24 days, and in (b) it was seen to be 17 days, leading to a predictability of 34 days: these values are related to an initial perturbation amplitude of 1°C.

These experiments were then repeated using a variable subgrid scale coefficient, depending on grid scale horizontal temperature gradient as described by Everson and Davies (1970). The results were; (a) working from a day of maximum K', the doubling time of error was reduced to 8 days, approaching the value obtained by primitive equation numerical models and corresponding to a predictability of 16 days; (b) working from a day of minimum K', the doubling time of error was 13 days, corresponding to a predictability of 26 days. The results in both cases show that predictability, as calculated from some initial phase of baroclinic development, is 50 per cent higher as measured from a maximum in K'compared with a minimum in K'. It also drops sharply with increase in the degree of model sophistication (expressed in the system discussed in this paper as variability of the subgrid scale coefficient).

P. J. Everson

Papers

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

Ekman boundary layer interactions in a numerical model of the general circulation

A note on the dependence of atmospheric predictability on baroclinic development