Studies of Transpiration in Relation to the Environment (5)

Abstract

In the previous paper (HASEBA and TAKECHI, 1972) various patterns of the change in transpiration with wind speed were analytically explained from the solution of the energy-budget equation of a plant leaf.In this paper, relations between the transpiration and the short-wave radiation are presented after the simulation of stomatal transpiration by taking into account the effect of insolation on stomatal aperture, and air temperature dependence of transpiration is also shown by reflecting over the joint effect of temperature on stomatal aperture. Further the obtained results are compared with some observations.When the leaf-moisture available for transpiration is sufficient, an equation of the stationary heatbudget of a leaf with equivalent stomata on both surfaces is written as follows:μRs+βL(Rl↓+Rl↑)-2βLσθL4=2hBΔθL+2LDTRΔCL, where Rs; short-wave radiation income, Rl↓ and Rl↑; long-wave radiation incomes from the upper atmosphere and the lower surroundings, respectively, and Rl↓=σ'ΘA6 and Rl↑ is approximated as βLσΘL4, ΘL and ΘA; temperatures of leaf and air(°K), respectively, ΔθL; temperature difference between leaf and air(°C), ΔCL=Co+C(ΔθL); water-vapor concentration difference of leaf interior from the surrounding air, Co; saturation deficit of air in concentration, C(ΔθL); correction term in vapor concentration difference due to temperature difference between leaf and air, μ and βL; leaf absorptivities of solar and thermal rediations, respectively, σ; Stefan-Boltzmann's constant, σ'=1.27×10-17ly/s°K6, L; latent heat of evaporation, hB=hn+hf; heat transfer coefficient for leaf surface, DTR=DLDB/(DL+DB); transpiration-transfer-coefficient, DL; internal transfer coefficient being a function of stomatal aperture, DB=Dn+Df; vapor transfer coefficient in boundary layer, hn, Dn; effects of buoyancy on the boundary layer transfer, both are functions of temperature difference between leaf and air and vapor concentration difference, hf, Df; forced-convection transfer coefficients including the effects of leaf-temperature variation over the surface and turbulent air-flow within a plant canopy.The heat-budget equation that contains unknown temperature difference between leaf and air in the terms of the outgoing long-wave radiation, free convection transfer and vapor-concentration difference was solved by using an analogue computer.Transpiraiton rate (w) is obtained by the following formula: w=2DTRΔCL.I. Relation between transpiration-rate and short-wave radiation.When internal transfer coefficient was a function of insolation, transpiration was calculated in the range of short-wave radiation between 0 and 1.5ly/min, for various values of relative humidities ranging from 20 to 100% under fixed conditions of air temperature from 0 to 40°C and wind speeds of 0.2 and 1m/s.Results obtained are as follows:1) Increasing insolation which enlarges stomatal opening increases the transpiration. This change in transpiration is relatively strongly dependent upon the changes in stomatal aperture.2) Except for the case of very low