Hilding Sundqvist

On Truncation Errors in Sigma‐System Models

Abstract A detailed examination is given as to how temperature T ‐ and thus geopotential ‐ of a synoptic state appears in sigma(σ)‐coordinate systems, i.e., systems whose lowest coordinate surface coincides with the earths surface. It is shown that the description of T along constant σ requires many more Fourier modes than would be expected by merely regarding the horizontal synoptic variation. This effect is related to the scale of the orographic field and to the vertical variation of T. With these results as a basis, possible truncation errors ‐ directly associated with the use of σ‐coordinates ‐ of horizontally discretized functions are discussed. It is found that if the resolution is inadequate, horizontal advection in the thermodynamic equation may become significantly distorted as a result of truncation. It is furthermore inferred that, with proper difference formulation of the terms of the pressure gradient force, it ought to be possible to limit ‐ though not to eliminate ‐ errors in this quantity...

Chapter 7 Parameterization of Clouds in Large-Scale Numerical Models

Publisher Summary This chapter discusses the general aspects of deducing a consistent cloud parameterization scheme, designed to predict fractional cloud cover and precipitation amounts and distribution in large-scale models. For specific background conditions, such as the supply of cloud condensation nuclei and large-scale and mesoscale circulations, the development of hydrometeors is governed by cloud microphysical processes. Cloud cover is determined by humidity and air motions, resulting from both the larger-scale background circulation and the release of latent heat on smaller scales. Owing to nonlinearities, the parameterizations of these two widely separated scale regimes are not completely decoupled. The chapter presents general formulations for the parameterizations of clouds in large-scale models. It is the value, or functional form, of the obtained parameters that account for different types or situations of condensation–cloud processes. Such differentiation is discussed with regard to both microphysical and subgrid-scale aspects. The chapter reveals that measurements provides the valuable data needed for testing algorithms used to relate measured radiances to cloud parameters.