Page 120 - Biosystems Engineering

Soil and W ater Conservation 101

Solar Radiation This is the energy from the sun reaching the earth.
Solar radiation is the main driving source for evaporation. When
radiation hits a surface some part is reflected back and some part is
absorbed. The fraction of reflected radiation is called albedo (α). For
fresh snow it is about 0.90, and for deep waters it is about 0.06. If the
incoming solar radiation is denoted as R , then the net radiation,
i
which is the net input at the surface, is given by
α
R = R (1 − ) − R e (3.4)
i
n
where R is radiation emitted by the body. All bodies emit radiation, which
e
depends on their temperature. According to the Stefan–Boltzmann law
e
R =⋅ ⋅σ T 4 (3.5)
e
where e is the emissivity (1 for a black box, 0.97 for water surfaces), σ
−8
4
2
is the Stefan-Boltzmann constant (5.67 × 10 W/m K ), and T is the
absolute temperature (K). The incoming radiation R is function of
i
scattering in the atmosphere, absorption by clouds, latitude, day of
the year, and time of the day.
3.4.2 Energy Balance Method for Estimating Evaporation
Consider the control volume shown in Fig. 3.5. In the figure, R is the
n
net solar radiation reaching the control volume [M/T ], H is the heat
3
3
conducted from the hot surface to the air [M/T ], G is the heat con-
3
ducted from the hot surface to the soil [M/T ], E is the latent heat
L
flux due to evaporation [M/T ], and Q is the amount of heat energy
3
stored within the control volume. Applying the conservation princi-
ple to the control volume, we can write
dQ
−
−
= R − G H E L (3.6)
n
dt
R n H E L

dQ/dt

G
FIGURE 3.5 Control volume of a small landscape for energy balance.