Bidirectional Thermal IR Model

Subroutine Bdrtm (cubdrtm.f)

This subroutine calculates the bidirectional thermal reflectance function for the canopy. It is calculated at 2 azimuth angles (the sun az angle and sun az + 180 deg) and NVZENP (input) zenith angles.

Four different types of IR canopy temperatures are calculated:

These temperature terms are defined in greater detail below.

Which type of temperature is calculated depends on the input value of FACTIR.

Outline

IR Temperature Terminology Defined:

from Norman, Chen & Goel (1990)

Average Vegetation Kinetic Temperature

The arithmetic mean of the temperatures of all the individual elements within the aerial portion of the canopy including flowers, stems and branches as well as leaves.

Hemispherical Infrared Temperature

The temperature calculated from the broad-band (3-100 u) thermal hemispherical flux density (Rir) emitted by the canopy (vegetation and soil) with a correction for sky thermal radiation (B) that may be reflected from the canopy. Therefore

Rir = ecpy*sigma*(Tir**4) + (1 - ecpy)*B

where ecpy is the broad-band, hemispherical, thermal emissivity of the canopy and sigma is 5.67x10**-8 W m-2K-4.

The thermal emissivity of the canopy is nearer to unity (blackbody) than the emissivity of a leaf because of multiple scattering and radiation trapping of the rough canopy surface. However, for a surface with a kinetic temperature of 300 K, assuming that surface to be a blackbody when in fact it had an emissivity of 0.99 would result in an inferred surface temperature 0.8 C below its actual temperature if the sky were clear. Thus, small uncertainties in canopy emissivity can lead to modest errors in the difference between inferred radiative temperature and kinetic temperature.

Average Directional Kinetic Temperature

This temperature is based on the assumption that leaves are black bodies, and the contributions of various leaf layers and soil are appropriately weighted by the fraction of view they occupy from the particular view direction. For a canopy of randomly positioned leaves, the fraction of view occupied by leaf layers and soil depends on the leaf angle distribution, leaf area index and view zenith angle and declines exponentially with depth in the canopy. When temperature gradients occur in the canopy or soil temperatures are different from leaf temperatures, the temperature of elements near the top of the canopy are most important in determining the average directional kinetic canopy temperature. In canopies of partial cover, the view zenith angle dependence of directional canopy temperature can be strong. Clearly this temperature can be very different from the average kinetic temperature.

Apparent Directional Infrared Temperature

This temperature is inferred from a measurement of thermal radiance with an infrared thermometer (IRT). Usually this measurement is made in a narrow wavelength band between 8 and 14 u. The dependence of sky flux density and leaf emissivity on wavelength can affect the interpretation of these measurements. Furthermore, temperature gradients within the plant-soil system, leaf area index, leaf angle distributions, sky thermal irradiance, leaf emissivity, sun angle, and view angle can all affect the relationship between apparent-infrared and kinetic temperatures.

The relationship between the average directional kinetic temperature and the apparent directional IR temperature is defined by the directional canopy emissivity, which can also be a function of many factors. Strictly speaking, directional canopy emissivity is a property of the canopy and is evaluated for isothermal conditions.... Effective directional canopy emissivity, which defines the relation between directional kinetic temperature and the apparent directional infrared temperature, also depends on the distribution of temperatures within the plant-soil system.

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