Truncation and use of model-coordinate data

The advantages and disadvantages of using global analyses on pressure level surfaces versus model (sigma or hybrid) level surfaces are explored. Model levels consist of a terrain-following coordinate in the lowest levels but may gradually transition to pressure with height. One major issue is that the model surface often does not correspond with the earth’s real surface. Another is that a change in horizontal resolution is not well defined because the vertical coordinate also changes in the process. However, such changes are required as comparison of analyses from one center with another or with model output requires a common vertical coordinate. Also, a reduction from high resolution with 106 waves (T106 resolution) to a moderate resolution with, say, 42 waves (T42), so as to reduce the size of datasets by a factor of about 6, is often desirable. Another issue involves the meaning and use of time averages on model surfaces and their relationship to corresponding time averages on pressure surfaces. The traditional representation on constant pressure surfaces has much to recommend it and is widely used and familiar to the community, but suffers from errors arising from interpolation to the pressure surfaces and the need to properly treat regions of those surfaces that are below ground (in regions of high topography). Spectral truncation and resolution changes are well defined on pressure surfaces. Test results are presented for cases where T106 analyses on model surfaces are (1) transformed to pressure and then truncated, (2) truncated and then transformed to pressure levels, and (3) then compared at comparable resolutions. The differences arise mainly from the ill-posed truncation on model surfaces, but also from vertical interpolations. These tests are also applied to a heat budget calculation involving nonlinear terms for one month. However, the latter comparison also brings in considerations of how best to do time averaging. Fortunately, in practical terms, differences between time-averaging approaches are quite small and probably negligible for most purposes. Other results show that truncation on model surfaces from T106 to T42 produces errors considerably larger than vertical interpolation errors. However, truncation to T63 for heat budget computations produces more acceptable, although not inconsequential, truncation errors provided that only T31 waves are retained as reasonably accurate.