### 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

*浦野, 慎一*

Permalink : http://hdl.handle.net/2115/49063

JaLCDOI : 10.14943/gbhu.75.91

#### Abstract

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 a new method was proposed based on the structures of equations. The PE equation has two terms. The first term X uses the decline of saturation vapor pressure curve Δ, and uses the parameter of γ/Δ ( γ is psychrometric constant) as a substitute for the actual Bowen ratio β. And the second term Υ uses the vapor pressure deficit Δe and wind function ｆ(u), and uses the parameter of Ea (=f(u)Δe) as a substitute for the actual flux caused by the actual vapor pressure difference. Because these of γ/Δ and Ea are the provisional parameters which differ according to reference height, both value of X and Y is also provisional in the estimation of evaporation rates. That is to say, the Penman equation has a structure that divides the evaporation rate into two parts, X and Y, and estimates each value using the provisional parameters γ/Δ and Ea, which are variables that change with changes in height. The Penman equation can be applied at any reference height if the wind function is known at that height. Under natural average conditions with a positive Bowen ratio, the constant Bowen ratio line in psychrometric chart is the shape of going to upper right. Therefore, the ratio of X to the whole rate increases as the reference height nears the surface. On the other hand, the PT equation consists of one term which has the structure of multiplying the first term X of PE equation by coefficient α. The α is a coefficient to correct the error due to ignore the second term Y of PE equation, and also to correct the difference of γ/Δ from actual Bowen ratio β. Hence, coefficient α is also provisional parameter which differ according to reference height. As it is clear from the characteristic of the X and Y of PE equation, and as Priestley and Taylor(1972) have already mentioned, if the reference height nears surface this α becomes to be nearly equal 1. This suggests that under natural average conditions of evaporation occuring, the Bowen ratio can be approximated γ/Δs (Δs is the decline of saturation vapor pressure curve at saturated surface). If we assume that the thin layer on the saturated surface has the Bowen ratio β as the form of the γ/Δs, the temperature and vapor pressure at any height should fall along the constant Bowen ratio line shown as Δs in the psychrometric chart. If so, the equations of PE and PT are resulted end in the equation of Bowen ratio method, and we can decide β from the observation data of only one height because we can easily estimate Δs using computer calculation. The advantage of this method are; only one point data at the height of z is needed, the wind speed data and wind function of PE equation are not needed, and coefficient α of PT equation become useless. 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 values calculated from the SBR method were close to those from the original Penman method and it was thus proven that this method has potential as an effective method for estimating evaporation rates more easily. The SBR method is on the basis of above assumption. Hence, it is necessary to confirm the effectiveness of assumption hereafter.

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