Modeling Concepts - Coastal Lagoons: Ecosystem Processes and Modeling for Sustainable Use and Development - page 263

where H SW is the absorbed short-wave radiation (range of 50-500 Wm −2 ); H H is the
long-wave back radiation from atmospheric constituents or dispersed solar radiation
(range of 30-450 Wm −2 ); H BSW and H BH are the short-wave solar radiation (range of
5-30 Wm −2 ) and dispersed solar radiation (range of 10-15 Wm −2 ), respectively,
reflected from the water surface; H B is the back long-wave radiation (range of
300-500 Wm −2 ); H L is a latent heat exchange (the energy loss due to evaporation is
within the range of order 100-600 Wm −2 ); and H S is the net heat flux due to
conduction or sensible heat transfer (with a range on the order of 50-500 Wm −2 ).
Net short-wave solar radiation (the first two terms of Equation (6.25)) varies
daily with the altitude of the sun, whose maximum depends on season, on dampening
by radiation scattering and absorption in the atmosphere, and on reflection from the
water surface:

HHa =⋅ ⋅ − ⋅

0

( RC ) (6.26)

SW t S a

where H 0 is the extraterrestrial radiation reaching the Earth's outer atmosphere.
depends on latitude of location and time. Date and time of day determine the sun
altitude, the sun-day duration, the standard times of sunrise and sunset, and the
relative distance between the earth and sun. a t is the fraction of the extraterrestrial
radiation reaching the water surface after reduction by scattering and absorption. It
depends on the dust coefficient, reflectivity of the ground, the moisture content, and
the optical air mass. R s is the albedo or the reflection coefficient, which depends on
the solar altitude and cloud cover, and C a is the fraction of solar radiation not
absorbed by clouds, which depends on the fraction of the sky covered by them.
Long wave radiation occurs when the atmosphere and clouds absorb part of the
solar radiation coming at the top of atmosphere ( H 0 ), become heated, and radiate
heat at longer wavelengths. The magnitude of long-wave radiation is computed using
the Stefan-Boltzman law modified for the emissivity of the air. It directly depends
on air temperature and atmospheric moisture, and is influenced by chemical con-
stituents of the atmosphere. The net long-wave radiation can be estimated from the
following empirical relation cited in Martin and McCutcheon 4b with the references
of Swinbank 7 and Wunderlich: 8

H SW

6

H =⋅ α 0 97 . ⋅ ⋅ σ ( T + 273 16 . ) ⋅ + ⋅ ( 1 0 17 . C ) (6.27)

H 0 a t

where α 0 is a proportionally constant with a value of 0.937 ⋅ 10 −5 , σ is the Stefan-

Boltzman constant of 5.67 10 −8 W m −2 (K) −4 , C t is the fraction of the sky covered

by clouds (0 < C t < 1), and T a (

⋅

C) is the air temperature measured at a height of
2 m above the water surface. Reflectance from the water surface is generally
assumed to be 3%.
Back radiation from the water is a black-body radiation type described using
the Stefan-Boltzman law, considering that water emissivity

°

ε w is approximately 0.97:

4

H =⋅ ⋅ εσ ( T + 273 16 . ) (6.28)

B w S