A four‐level, quasi‐geostrophic, β plane, general circulation numerical model is developed, initially without a simulated boundary layer, and the sensitive dependence of large scale flow characteristics on the numerical choice of essential parameters (non‐adiabatic heating funnctions, static stability values, and internal turbulent stresses) is noted in a number of long period (100 day) integrations. It is particularly interesting to note that unless the values of turbulent stress coefficients are sufficiently large, the characteristic structures of cyclone waves and eddy kinetic energy functions are lost and these become random flow patterns and functions.
In order to obtain a lower limit estimate of the sensitivity of dependence of large scale flow model characteristics on the presence of a planetary boundary layer, a simple constant ‘height’ (from 1 000 to 900 mb) ‘Ekman boundary layer’ is then introduced, an analytic solution of the linearised boundary layer equations being matched to the numerical model through the vertical velocity field at the model grid points. The effect of this introduction on the structure of the meridional circulation is very marked, and the magnitude of this circulation is seen to depend quite sharply on the numerical value chosen for the model boundary layer eddy viscosity. It is also found that the most realistic large scale flow characteristics are reproduced with a boundary layer present, when the free atmosphere turbulence (vertical) stress coefficients are reduced to quite small values.
The four‐level model described by Searle & Davies (1975) in an accompanying paper was integrated for a 100 days period using (a) the (Chilton, U.K.) Atlas Computer, (b) the I.B.M. 360/195 at Harwell, U.K., with firstly single precision and secondly double precision; identical finite difference schemes and computer programmes were applied and also identical initial data employed in each of the three cases. The computed eddy kinetic energy function in (a) diverged quickly from those in (b) after about 400 time steps of ½ hour duration. After about 1 500 time steps of the same duration the single and double precision results in (b) also diverged quite sharply and the energy functions were out of phase after a further 1 000 time steps. The implication is that the effect of truncation and other errors at the grid points of numerical models on the exact timing of large scale dynamics is very serious, and presents a formidable mathematieal‐physical‐computing probem. This must be solved before accurate long period weather predictions may be achieved.
The four-level model described by Searle t Davies (1975) in an accompanying paper was integrated for a 100 days period using (a) the (Chilton, U.K.) Atlas Computer, (b) the I.B.M. 360/195 a t Harwell, U.K., with firstly single precision and secondly double precision; identical finite difference schemes and computer programmes were applied and also identical initial data employed in each of the three cases. The computed eddy kinetic energy function in (a) diverged quickly from those in (b)
A four-level, quasi-geostrophic, B plane, general circulation numerical model is developed, initially without a simulated boundary layer, and the sensitive dependence of large scale flow characteristics on the numerical choice of essential parameters (non-adiabatic heating fnnctions, static stability values, and internal turbulent stresses) is noted in a number of long period (100 day) integrations. It is particularly intoresting to note that unless the values of turbulent stress coefficients are sufficiently large, the characteristic structures of cyclone waves and eddy kinetic energy functions are lost and these become random flow patterns and functions.In order to obtain a lower limit estimate of the sensitivity of dependence of large scale flow model characteristics on the presence of a planetary boundary layer, a simple constant 'height' (from 1000 to 900 mb) 'Ekman boundary layer' is then introduced, an analytic solution of the linearised boundary layer equations being matched to the numerical model through the vertical velocity field at the model grid points. The effect of this introduction on the structure of the meridional circulation is very marked, and the magnitude of this circulation is seen to depend quite sharply on the numerical value chosen for the model boundary layer eddy viscosity. It is also found that the most realistic large scale flow characteristics are reproduced with a boundary layer present, when the free atmosphere turbulence (vertical) stress coefficients are reduced to quite small values.
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