SUMMARYNurnciical experiments with a two-level, quasi-geostrophic mtxlel, described by Davies arid Davies (1900), have been extended in several ways; the grid spacing of the previous model has been halved, greatly rcducing 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 o l Ixiroclinic 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 thc 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 surfxes, 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 becn 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 ol Northern Hemisphere synoptic charts for the winter of 1956-57, which include a well-formed blocking sitiration. Estimates of eddy kinetic energy were made for both surface and 500 mb charts for the sections (a) between 50"W and GOOE, (b) between 1lO"W and l W 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 2R December, the behaviour of K' ( t ) over this period bcing 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 represcntation. In the first instance, this is taken in the often-used form AF2 u. where u is the appropriate velocity component and A is an invariant of space and time; in the second ca...
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).
SUMMARYA 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).
In order to determine cLimatic evoLution on a seasonaL time scaLe, an understanding of the dynamics of the pLanetary waves is essentiaL. At Exeter research is centered on using G.C.M.'s to investigate the factors infLuencing the phasing and ampLitudes of these waves. There are two Lines of approach in appLying G.C.M.'s to cLimate study. The first is to use a highLy detaiLed modeL in which the effect of anomaLies (e~g. SST anomaLies) as the net resuLt of the compLex feedback mechanisms within the modeL are evaLuated. WhiLe this method is satisfying from the point of view that LittLe is omitted from the modeL which ~muLates the reaL atmosphere to a cLose approximation, it has the drawbacks of being expensive in computer time and it can be difficuLt to perceive the mechanisms behind the resuLtant teLeconnections. The second approach, which is adopted here, is to use a simpLified G.C.M. in which the physics are highLy parameterised and examine how various forcings act both separateLy and together.RecentLy our interest has focussed on the investigation of atmospheric modes. A mode here is taken to mean a cLimatic regime in which the pLanetary waves (wave numbers 1 ~ 4) show persistence to systematic evoLution over an extended period of time. The muLtipLe equiLibria soLutions for barotropic fLow demonstrate that the simpLified atmospheric equations possess mode type soLutions (Charney and Devoren 1979) and for the reaL atmosphere, there is some suggestion that mode type behaviour exists during the winter evoLution; it has been found that the orientation of the 200 mb. October-November circum-polar vortex during the spin up period can be used as a reasonable indicator for the severity of the subsequent winter (Reeve, 1982, Murdoch andDavies, 1983). The orientation condenses, in an empiricaL manner, the information concerning the phasing of the pLanetary waves. Given that Less simpLified systems than the barotropic wiLL aLso possess mode type soLutions and that the reaL atmosphere does, the question arises, what are the determinants of a particuLar mode ?It is possibLe that knowLedge of past cLimate can heLp to answer this question. Different modes have existed on MiLankovitch time scaLes where the soLar insoLation and aLso, presumabLy, mean gLobaL temperature were different. What might be more usefuL to aid the understanding of the present cLimate wouLd be a knowLedge of the gLobaL cLimate within the Last thousand uears when the externaL forcings remain approximateLy constant but the internaL distributions of anomaLies are different from today. Thus the summers and winters of the LittLe Optimum and LittLe Ice Age, for exampLe, are of interest since they may represent extreme soLutions for the present set of cLimatic parameters.In order to investigate the determinants of the soLutions for the present climate parameters, several numerical experiments have been undertaken using a two-LeveL quasi geostrophic, U co-ordinate hemispheric spectraL modeL. The aim of the experiments described beLow has been to examine how the or...
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