266
The Light Environment of Plant Canopies
that Kbe(@) refers to the extinction coefficient for beam radiation and
Kbe(0) refers to the extinction from the nadir view direction. Kbe(0) is
never used in the following equations to refer to the direction of the sun.
Although similar equations are used to describe sun and view effects, the
context should always be obvious.
From Eq. (15.22), the fraction of leaves at depth L in a canopy that
is sunlit is given by exp(- Kbe(@)L). If the sensor is placed at the same
zenith and azimuth angles as the sun, and for discussion purposes assume
the sensor is so small that it casts a negligibly small shadow, then the
sensor would view exactly these sunlit leaves. Thus the same exponential
expression can be used to estimate sunlit-leaf-area fraction as to estimate
the fraction of leaves in a layer than can be viewed from the same direction.
The special case of identical sun and view directions is referred to as the
canopy hot spot, because the canopy appears brighter from this direction
then any other direction; all the leaves being sunlit from this direction.
For this special case, sunlit leaves and shaded leaves cannot be assumed
to be independent because both sun and view directions share the same
path through the canopy. As the sensor is moved off the direction of the
sun, shaded leaves occupy an increasing fraction of the sensor FOV until
the view path and the path of the sun rays are independent. The decrease
in radiance as a function of the increasing angle between the direction of
the sensor and the sun direction depends on LAI, leaf angle distribution,
leaf size, sun zenith angle, and canopy height (Kuusk, 1995). Typically
the hot spot varies from a few degrees wide to a few tens of degrees wide
depending on conditions. The equations that follow, which pertain to
nadir viewing only, do not consider the hot spot. Hot spot considerations
generally would represent a minor refinement for latitudes where the sun
zenith angle is rarely less than 20".
A remote sensor that is directed toward a canopysoil systemmay view
both vegetation and soil. For a canopy of randomly positioned leaves, the
fraction of the sensor view that is occupied by soil is exp(- Kbe(0) L,) SO
that the fraction of view occupied by vegetation is 1 - exp(- Kbe(0) Lr).
The vegetation portion of the view consists of both sunlit and shaded
leaves. The fraction of leaves at a depth L that is sunlit with the sun at
zenith angle @ is given by Eq. (15.22). Therefore the fraction of leaves
at a depth L that is sunlit and can be viewed from nadir is given by the
product: exp(- Kbe (0)L) exp(-Kbe (@)L). If the product of these two
exponentials is integrated over the depth of the canopy L, the sunlit leaf
area index is obtained that is in the view of the sensor, L*, :
The fraction of the sensor view occupied by sunlit leaves is given by the
projection of L*, in the direction of the sensor or fV,sl = L*, Kbe(0).
The fraction of sensor view occupied by shaded leaves is the difference
between the view fraction occupied by vegetation (1 - exp(- Kbe(0) L,))
The Light Environment of Plant Canopies
that Kbe(@) refers to the extinction coefficient for beam radiation and
Kbe(0) refers to the extinction from the nadir view direction. Kbe(0) is
never used in the following equations to refer to the direction of the sun.
Although similar equations are used to describe sun and view effects, the
context should always be obvious.
From Eq. (15.22), the fraction of leaves at depth L in a canopy that
is sunlit is given by exp(- Kbe(@)L). If the sensor is placed at the same
zenith and azimuth angles as the sun, and for discussion purposes assume
the sensor is so small that it casts a negligibly small shadow, then the
sensor would view exactly these sunlit leaves. Thus the same exponential
expression can be used to estimate sunlit-leaf-area fraction as to estimate
the fraction of leaves in a layer than can be viewed from the same direction.
The special case of identical sun and view directions is referred to as the
canopy hot spot, because the canopy appears brighter from this direction
then any other direction; all the leaves being sunlit from this direction.
For this special case, sunlit leaves and shaded leaves cannot be assumed
to be independent because both sun and view directions share the same
path through the canopy. As the sensor is moved off the direction of the
sun, shaded leaves occupy an increasing fraction of the sensor FOV until
the view path and the path of the sun rays are independent. The decrease
in radiance as a function of the increasing angle between the direction of
the sensor and the sun direction depends on LAI, leaf angle distribution,
leaf size, sun zenith angle, and canopy height (Kuusk, 1995). Typically
the hot spot varies from a few degrees wide to a few tens of degrees wide
depending on conditions. The equations that follow, which pertain to
nadir viewing only, do not consider the hot spot. Hot spot considerations
generally would represent a minor refinement for latitudes where the sun
zenith angle is rarely less than 20".
A remote sensor that is directed toward a canopysoil systemmay view
both vegetation and soil. For a canopy of randomly positioned leaves, the
fraction of the sensor view that is occupied by soil is exp(- Kbe(0) L,) SO
that the fraction of view occupied by vegetation is 1 - exp(- Kbe(0) Lr).
The vegetation portion of the view consists of both sunlit and shaded
leaves. The fraction of leaves at a depth L that is sunlit with the sun at
zenith angle @ is given by Eq. (15.22). Therefore the fraction of leaves
at a depth L that is sunlit and can be viewed from nadir is given by the
product: exp(- Kbe (0)L) exp(-Kbe (@)L). If the product of these two
exponentials is integrated over the depth of the canopy L, the sunlit leaf
area index is obtained that is in the view of the sensor, L*, :
The fraction of the sensor view occupied by sunlit leaves is given by the
projection of L*, in the direction of the sensor or fV,sl = L*, Kbe(0).
The fraction of sensor view occupied by shaded leaves is the difference
between the view fraction occupied by vegetation (1 - exp(- Kbe(0) L,))