Two itcsrativc mt+hods are driscribcd for obtaining horizontal winds from the pressure-height field by means of higher-order grostrophic approximations for the purposc of improving up011 thcl geostrophic wind. The convergence propert,ies of the iterative. mtxthods are discussed; nnd in :t simplcx theoretical case, one of the methods is found to diverge with strong cyclonic motion. Both iter:ttivc mcthods were applied to analyzed 500-mb. height charts and over most of thr map convergd in a few scans to wind values somewhere between the geostrophic wind and the wind obtairlrd from the balance rqnation. Howe~ve~r i n a few locations continued iteration led t o increasing differences betwecn successively computed winds: i.c.., the methods appc,ared to diverge. In fact, wind values in adjacent areas gradually tended to be corrnptcd. This lack of convergtance, occurring mainly in areas of negative vorticity and additionally i n t,he case of mrthod I1 in are'as of strong cyclonic vorticity, was associated with the development of excessive horizontal wind divergence, which after three. or four iterations sometimes exceeded the relative vorticity.Stream functions were computed by rtlaxing the. relative vorticity of the winds obtained by methods I and 11, generally after one itcration. These \?-ere compared to thv stream function obtained by solving t,hcl balance equation and no significant differences were noted. 13arotropic fortac:tsts prepurcd from the stream functions derived from the two methods are essentially the same as forecasts with the, stro:rtn fullction obtaintd from t,he balance equation.
Height normals for 1,000, 700 and 500 mb, published by U.S. Weather Bureau, have been used to study the normal temperature field of the 1,000—500 mb layer by means of a simple model. In this model the normal temperature-height curve is replaced by one having a temperature lapse-rate independent of height in such a way that the thicknesses of the sub-layers 1,000—700 and 700—500 mb are correctly represented by the model. As a consequence, the temperature as well as its horizontal gradient and the thermal wind all have a linear variation with height and may be described in terms of two parameters, the temperature lapse-rate k and a “representative” 1,000 mb temperature τ0.
Hemispheric maps for these parameters as well as the thermal wind at 1,000 and 500 mb have been prepared for the months January and July. The major frontal zones of the atmosphere appear clearly on the τ0-maps in positions which agree essentially with those shown earlier by a number of meteorologists. The July map reveals, however, a strong baroclinic zone in high latitudes, surrounding the polar cap, not shown clearly in earlier presentations of the low-level baroclinity.
The k-charts disclose large horizontal variation in the temperature lapse-rate, and the charts for the thermal wind show that its variation with height is very pronounced in middle and high latitudes.
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