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In this chapter we present some of the physical processes that are used in numerical weather prediction modeling. Grid-point models, based on finite differences, and spectral models both generally treat the physical processes in the same manner. The vertical columns above the horizontal grid points (the transform grid for the spectral models) are the ones along which estimates of the effects of the physical processes are made. In this chapter we present a treatment of the planetary boundary layer, including a discussion on the surface similarity theory. Also covered is the cumulus parameterization problem in terms of the Kuo scheme and the Arakawa- Schubert sheme. Large-scale condensation and radiative transfer in clear and cloudy skies are the final topics reviewed. There are at least three types of fluxes that one deals with, namely momentum, sensible heat, and moisture. Furthermore, one needs to examine separately the land and ocean regions. In this section we present the socalled bulk aerodynamic methods as well as the similarity analysis approach for the estimation of the surface fluxes. The radiation code in a numerical weather prediction model is usually coupled to the calculation of the surface energy balance. This will be covered later in Section 8.5.6. This surface energy balance is usually carried out over land areas, where one balances the net radiation against the surface fluxes of heat and moisture for the determination of soil temperature. Over oceans, the sea-surface temperatures are prescribed where the surface energy balance is implicit. Thus it is quite apparent that what one does in the parameterization of the planetary boundary layer has to be integrated with the radiative parameterization in a consistent manner.

Any land surface that receives regular rainfall is almost certain to be covered by vegetation. Most of the inhabitable regions of the globe fall into this category. Often the vegetation is tall enough to call into question the assumption, implicit in the discussion of the first two chapters, that the roughness elements on the ground surface are much lower than any observation height of interest to us. In fact, if we venture to make measurements too close to tall vegetation, we discover significant departures from many of the scaling laws and formulas that seem to work in the surface layer above the canopy. To take one example, momentum is absorbed from the wind not just at the ground surface but through the whole depth of the canopy as aerodynamic drag on the plants. Consequently, although we still observe a logarithmic velocity profile well above the canopy, its apparent origin has moved to a level z = d near the top of the plants. The precise position of this “displacement height,” d, depends on the way the drag force is distributed through the foliage and this in turn depends on the structure of the mean wind and turbulence within the canopy. Our interest in the nature of within-canopy turbulence, however, is not motivated solely by its influence on the surface layer above. The understanding of turbulent transfer within foliage canopies provides the intellectual underpinning for the physical aspects of agricultural meteorology. As such it has a history almost as venerable as investigations of the surface layer itself. The landmark study of Weather in Wheat by Penman and Long (1960) was the first of a series of seminal papers to establish the quantitative link between the turbulent fluxes in a canopy and the physiological sources and sinks of heat, water vapor, and carbon dioxide (CO2). Prominent and influential among these early publications were those by Uchijima (1962), Denmead (1964), Brown and Covey (1966), and Lemon and Wright (1969). Whereas these authors were motivated by curiosity about plant physiology and the transfer of water and other scalars through the soil-plant-air continuum, other workers forged the link between the classical surface layer studies detailed in Chapter 1 and the structure of within-canopy turbulence.