Further work with the Bushby‐Timpson 10‐level model

Abstract

SUMMARYVertical smoothing of the initial height fields proved to be a crucial step in obtaining 24 hr forecasts using the 10-level primitive equation model (Bushby and Timpson 1967) on any set of data : the particular operator used and the effects on the forecast fields are described. The latent heat effect is examined quantitatively by comparing two 24 hr forecasts, one of which included and the other excluded the contribution of the latent heat of condensation. The forecast fields obtained when a larger grid length is used, in conjunction with an appropriately lengthened time-step, are compared with forecasts obtained from the basic grid length and time-step and the implications arising from the increase of scale are discussed. VERTICAL SMOOTHING OF THE INITIAL HEIGHT FIELDS(a) The problem Bushby and Timpson (1967) described a 10-level primitive equation model of the atmosphere and discussed the results of one 24 hr forecast. Considerable difficulty was experienced when attempts were made to obtain another 24 hr forecast owing to the smallscale roughness which developed during the integration, especially in the vertical motion fields. Some roughness had also been noted in the first 24 hr forecast but in that case the roughness had not prevented the computations from proceeding to the full 24 hours.The procedure followed in preparing the initial height data on which the first 24 hr forecast was based was as follows. The basic height data consisted of grid point values extracted from upper air contour charts at 1,000, 850, 700, 500, 400, 300, 200 and 100 mb. These height fields were then horizontally smoothed using a three point smoothing operator of the form where Ht", H$ are the smoothed and unsmoothed heights respectively at grid point i and Ht-1, H~+ I are the unsmoothed heights at the adjacent grid points in the direction along which the smoothing operation is being carried out. The smoothing operation was applied along each of the x , y directions using a = 4 and the process was then repeated using a = -+ ; a s explained by Wallington (1962) such a procedure decreases the amplitudes of the smaller scale features which it is desired to eliminate, leaving the larger scale features not greatly altered. No other smoothing was carried out on the initial height data for the first 24 hr forecast, the 900, 800 and 600 mb height fields being obtained by interpolation from those at 1,000,850,700 and 500 mb. The above procedure proved to be unsuccessful when attempts were made to obtain 24 hr forecasts for other occasions and a close examination of the lapse rates derived from the height fields showed that there were on all occasions some parts of the chart where the derived lapse rates were super dry adiabatic. For the initial data for 0000 GMT 1 December 1961, the occasion of the first forecast, such parts were rather small and the lapse rates did not greatly exceed the dry adiabatic lapse rate,

problems and promises of deterministic extended range forecasting1

“…On the other hand, only their statistical properties would be of importance for longer periods. In part, I think this has already been demonstrated by the high resolution experiments conducted by Bushby and his associates (e.g., Burwell and Timpson, 1968) at the British Meteorological Office. This therefore implies, that a very high resolution observation network is more critical for the short range forecast.…”

A Harmonic-Fourier Spectral Limited-Area Model with an External Wind Lateral Boundary Condition*

“…One is the boundary consistency problem, which concerns whether the variables at the boundary predicted by two models are compatible (or continuous) with each other at the same time step t ϭ t 0 ϩ ⌬t. The boundary treatments studied by Benwell et al (1971), Okamura (1975), and Davies (1976) are all aimed at solving this consistency problem, but the external wind lateral boundary method is very effective for this purpose.…”

“…The harmonic function added to the inner part cannot cause any discontinuity near the boundary. Thus, the new boundary method is quite different from some other artificial pragmatic techniques (Benwell et al 1971;Okamura 1975;Davies 1976) mentioned above, and it has a relatively strong theoretical basis, especially for the wind field. Tests of this boundary method will show that the predicted motion near the boundary is smooth without any other boundary treatment.…”

“…To reduce the amplitude of spurious solutions near the boundary due to ill-posed boundary conditions, it is necessary to employ a lateral boundary treatment that can effectively reduce lateral boundary noise during the integration. These methods include the insertion of a highly diffusive layer contiguous to the boundary (Benwell et al 1971), a divergence control method (Okamura 1975), a method of modification of the tendencies at the boundary (Kesel and Winninghoff 1972;Perkey and Kreitzberg 1976), the boundary relaxation method (Davies 1976), etc. In the limited-area spectral models of Tatsumi (1986) and Juang and Kanamitsu (1994), the boundary relaxation method is used to reduce the lateral boundary noise.…”

Numerical Prediction of Tropical Weather Systems

“…Since the Shuman (1962) finite-difference scheme utilizes nine points, the u and v components of the mind were held constant on the two outer rows during the forecast cycle; the normal and tangential minds were then adjusted on the two outer rows and columns so that the areal means of the divergence and the vorticity for the entire grid were equal to those inside the region where the winds were forecast. To further constrain the amplification of spurious waves near the lateral boundaries, we applied a high lateral viscosity proposed by Benwell and Timpson (1968) to the third and fourth rows and columns in from the boundary. These constraints resulted in stable boundary conditions.…”