ペンマン式およびプレストリ・テーラ式のボーエン比に関する考察 (池田隆司教授記念号)
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概要
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The bowen ratios shown in the Penman(1948)(PE) and Priestley-Taylor(1972)(PT) equations,widely used to estimate evaporation rate from saturated surface, were studied theoretically, and anew method was proposed based on the structures of equations. The PE equation has two terms. The first term X uses the decline of saturation vaporpressure curve Δ, and uses the parameter of γ/Δ ( γ is psychrometric constant) as a substitutefor the actual Bowen ratio β. And the second term Υ uses the vapor pressure deficit Δe andwind function ｆ(u), and uses the parameter of Ea (=f(u)Δe) as a substitute for the actual fluxcaused by the actual vapor pressure difference. Because these of γ/Δ and Ea are the provisionalparameters which differ according to reference height, both value of X and Y is also provisionalin the estimation of evaporation rates. That is to say, the Penman equation has a structurethat divides the evaporation rate into two parts, X and Y, and estimates each value using theprovisional parameters γ/Δ and Ea, which are variables that change with changes in height. ThePenman equation can be applied at any reference height if the wind function is known at thatheight. Under natural average conditions with a positive Bowen ratio, the constant Bowen ratioline in psychrometric chart is the shape of going to upper right. Therefore, the ratio of X to thewhole rate increases as the reference height nears the surface. On the other hand, the PT equation consists of one term which has the structure ofmultiplying the first term X of PE equation by coefficient α. The α is a coefficient to correctthe error due to ignore the second term Y of PE equation, and also to correct the differenceof γ/Δ from actual Bowen ratio β. Hence, coefficient α is also provisional parameter whichdiffer according to reference height. As it is clear from the characteristic of the X and Y of PEequation, and as Priestley and Taylor(1972) have already mentioned, if the reference height nearssurface this α becomes to be nearly equal 1. This suggests that under natural average conditionsof evaporation occuring, the Bowen ratio can be approximated γ/Δs (Δs is the decline ofsaturation vapor pressure curve at saturated surface). If we assume that the thin layer on the saturated surface has the Bowen ratio β as the formof the γ/Δs, the temperature and vapor pressure at any height should fall along the constantBowen ratio line shown as Δs in the psychrometric chart. If so, the equations of PE and PT areresulted end in the equation of Bowen ratio method, and we can decide β from the observationdata of only one height because we can easily estimate Δs using computer calculation. Theadvantage of this method are; only one point data at the height of z is needed, the wind speeddata and wind function of PE equation are not needed, and coefficient α of PT equation becomeuseless. In this study, this method was proposed as the name of Surface Bowen Ratio (SBR)method, and it was verified using data from two lakes, Hokkaido, Japan. The resulting valuescalculated from the SBR method were close to those from the original Penman method and itwas thus proven that this method has potential as an effective method for estimating evaporationrates more easily. The SBR method is on the basis of above assumption. Hence, it is necessaryto confirm the effectiveness of assumption hereafter.
- 北海道大学大学院理学研究院自然史科学部門（地球物理学）の論文
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