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Some improvements in calculating the plant stand surface albedo and its influence on ground surface temperature

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It is shown that better results are obtained in calculating the surface albedo of a plant stand for near-infrared solar radiation using the modified two-stream approximation in favor of the Schwarzschild one. These evaluations of the plant stand surface albedo were obtained by assuming the values for scattering parameters of upward β0 and diffusive β solar radiation in the plant stand, by applying the delta-Eddington approximation. However, more accurate evaluations of β0 and β can be obtained by using Rayleigh's phase scattering functions for radiative scattering in a plant stand. Furthermore, much attention is devoted to testing the influence of the plant stand albedo for the visible part of solar radiation (for which the Schwarzchild approximation is valid) on ground surface temperature. The ground surface temperature was calculated by the “force-restore” method; the greatest ground surface temperature corrections were obtained in cases where the surface beneath the plant stand is covered with snow. The influence on ground surface temperature of high absorption and scattering in dense plant stands with horizontal foliage was also tested. Again significant corrections of ground surface temperature were obtained, taking into consideration the given characteristics of a plant stand compared to a standard albedo value.

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A :

albedo of direct radiation in plant canopy

A D :

albedo of diffuse radiation in plant canopy

A p :

albedo of the ground surface

A Q :

total albedo in plant canopy

a :

proportion of gaps in plant canopy α characteristic of surface evaporation

α w :



parameter of upward scattering diffuse radiation

β0 :

parameter of upward scattering direct radiation

C g :

soil volumetric heat capacity

C p :

air specific heat

C DH :

aerodynamic transfer coefficient for heat

C DE :

aerodynamic transfer coefficient for moisture

d :

depth of soil


sun's declination


azimuth of incident radiation


azimuth of diffuse radiation


characteristic of the radiative sources

G :

foliage orientation function

g :

parameter in delta-Eddington approximation

g z :

parameter for near-infrared radiation

ГL :

scattering phase function radiation

γ D :

diffuse solar radiation flux

γ G :

soil heat flux

γ H :

air sensible heat flux

γ L :

air latent heat flux

γ O :

solar constant

γ R :

net longwave radiation flux

γ S :

direct solar radiation flux

h o :

height of the sun

i :

intensity of diffuse radiation

k :

von Karman constant

L :

leaf area index

L v :

coefficient for latent heat of evaporation

λ g :

soil heat conductivity

n/N :

relative cloudiness


solid angle


frequency of temperature wave

Q a :

specific humidity of air

Q w :

specific humidity of saturated air

R L :

coefficient of plant reflectivity

r :

direction of diffuse radiation

ŕ :

direction of incident radiation

r o :

direction of solar radiation

r s :

resistance of the leaf stomata

p o :

air density

S :

intensity of direct solar radiation


Stefan-Boltzman constant

T a :

air temperature

T G :

ground surface temperature

T c :

cloud temperature

T 1 :

feaf temperature

T * :

air temperature scale

t :


Δt :

time step


zenith angle of diffuse radiation


zenith angle of incident radiation

ϑ0 :

zenith angle of solar radiation

U * :

friction velocity scale

V :

near-surface wind velocity

W g :

soil water content

W L :

scattering coefficient in plant canopy

W sat :

saturated soil water content

z :

vertical direction


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Unkaševié, M. Some improvements in calculating the plant stand surface albedo and its influence on ground surface temperature. Int J Biometeorol 33, 184–195 (1989).

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Key words

  • Albedo
  • Scattering parameter
  • Leafarea index
  • Ground surface temperature
  • Diffuse radiation