CHAPTER 4 HEAT BALANCE OF BARE GROUND

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60 CHAPTER 4n∑j=1view factor(i, j) = 1 (4.15)Figure 4.11. Radiation exchange amongthe sky, the ground and a building.Figure 4.12. Geometrical representation ofview factor.which means that the summation of the view factors of the arbitrary surface i to anysurface j including itself is equal to 1. The self view factor is defined when thesurface is concave.If we look at protected cultivation systems closely, most parts of the systems arenot flat surfaces. Rows, tunnels and houses all have curved surfaces of differenttemperatures. Therefore, it is important to consider view factors in detailedanalyses of these systems. However, in the present book, in order to simplify theproblem, view factors are not taken into account in any model; it is assumed that allsurfaces are infinitely flat. View factor analyses have been conducted in somemodels (e.g., Takakura et al., 1971), which can be consulted when necessary.
HEAT BALANCE OF BARE GROUND 61Table 4.1. Emissivities of various surfaces (after Seller, 1965).A. Water and Soil Surfaces C. VegetationWater 0.92-0.96 Alfalfa, dark green 0.95Snow, fresh fallen 0.82-0.995 Oak leaves 0.91-0.95Ice 0.96 Leaves and plantsSand, dry light 0.89-0.90 0.8 µm 0.50-0.53Sand, wet 0.95 1.0 µm 0.50-0.60Gravel, coarse 0.91-0.92 2.4 µm 0.70-0.97Limestone, light gray 0.91-0.92 10.0 µm 0.97-0.98Concrete, dry 0.71-0.88 D. MiscellaneousGround, moist, bare 0.95-0.98 Paper, white 0.89-0.95B. Natural Surfaces Glass, pane 0.87-0.94Desert 0.90-0.91 Bricks, red 0.92Grass, high dry 0.90 Plaster, white 0.91Fields and shrubs 0.90 Wood, planed oak 0.90Oak woodland 0.90 Paint, white 0.91-0.95Pine forest 0.90 Paint, black 0.88-0.95Paint, aluminum 0.43-0.55Aluminum foil 0.10-0.5Iron, galvanized 0.13-0.28Silver, highly 0.20polishedSkin, human 0.954.7. LONG WAVE RADIATIONRadiation is emitted from any body whose temperature is above 0 K, including thesky and the earth's surface. Radiation emitted from a body whose temperature is inthe ordinary range (0 – 30 o C) has a peak of density in the longer wavelengths shownin Fig. 4.13 called long wave radiation.Emissivity and temperature of the atmosphere are not simple to determine;neither is long wave radiation from the sky. Within a rather thin layer such as 10 mor so, it can be assumed that the air is transparent to long wave radiation. Thisassumption, however, cannot be applied to the whole layer of the atmosphere aroundthe earth. Atmospheric radiation is a function of water vapor, carbon dioxide andozone content, but in most cases, the effects of carbon dioxide and ozone areneglected, mainly because of their thin, very low emissivities.A large number of radiation charts have been developed for computingatmospheric radiation (e.g., Seller, 1965). They need data that are not available,and the techniques for computing the radiation are not simple. Empirical equations,which are less accurate, are more practical. Brunt’s equation (in van Wijk, 1966) is
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