Article,

Leaf temperatures during radiation frost Part II. A steady state theory

.
Agricultural and Forest Meteorology, 42 (2-3): 135--155 (March 1988)
DOI: 10.1016/0168-1923(88)90073-1

Abstract

Leaf and ground surface energy budgets were solved to predict equilibrium temperatures of isolated leaves (T1) on nights of radiation frost as a function of air, screen and ground temperatures and of leaf size and position above ground. A set of non-linear equations describes the interaction of leaf and ground temperatures through radiation exchange when shading of the ground by the leaf is important. Numerical techniques were used to obtain the solutions. A simple equation was also presented for T1 when shading is unimportant. Shading influenced ground surface temperature by up to 8°C for relatively poor thermal conductors, such as a grass sward, but by only \~ 2°C for a better conductor such as mineral soil. In the absence of wind, changes in T1 as a result of shading were predicted to be + 1.5°C and + 1.0°C for leaves 0.10 and 0.01 m wide, respectively, when displayed above a grass sward. Smaller changes in T1 were predicted for leaves above mineral soil and when forced convection replaced free convection as the mechanism of heat transfer to the leaf. Comparison of predicted and observed leaf temperatures was satisfactory for both the small leaves of Eucalyptus viminalis and for the larger E. pauciflora leaves provided forced convection was assumed in calculating the leaf boundary layer transfer coefficient. Free convection did not contribute significantly to heat transfer, even under the still conditions of a nocturnal inversion during clear nights. Predictions of T1 assuming free convection thus represent the extreme minima to be expected. Both sensible and latent heat are transferred to a leaf when T1 is equal to or less than the dew or frost point of the air. Only sensible heat is transferred above this temperature. Predictions using linear theory showed that leaves without frost were 1-2°C colder than those with frost at a wind speed of 0.2 ms-1.

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