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《Geographical Research》 1987-02
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AN ARIDITY INDEX BASED ON ENERGY BALANCE

Tang Dengyin(Institute of Geography, Chinese Academy of Sciences, and State Planning Commission of the People's Republic of China)  
A long history has been experienced to research into the geographical aridity and humidity by use of various indices, This paper briefly reviewed some typical indices in the climatic classifications such as Koppen's, Thorn th-waite's and Budyko's types. Summing up, the indices were gradually developed from empirical, semi-empirical description to physics-based method.it is an opportunity to derive new index as the achievements of earth sciences such as energy balance, water balance and related technique, have been made in the last decades.An attempt has been made to transfer some concepts by Monteith and Jackson et al into the field of geographical classification which is one of the most important branches in Geography. In this paper soil water stress index (SWSI) which more closely related to soil water status, was used to indicate aridity and humidity. Based on the fact that the ratio of actual evaporation Ea to potential evaporation Eo depends on the availability of soil water, SWSI Can be defined asand vanes from 0 (extremely humid) to 1(extremely arid) .Kn皐ing E, from Penman formulaand Ea from Penman-Monteith formulaand defining potential evaporation as the evaporation with no restriction of water supply under existing meteorological condition, SWSI can be written as where r——psychrometer constant, △——slope of saturation vapour pressurewith temperature,and rs /ra——ratio of soil resistance to vapour transfer rs to airdynamic resistance r . For SWSI only the term rs/r4 needs to be answered.Like the derivation of Penman formula and Penmam-Monteith fomula from the combing tion of energy balance equation, sensible heat equation and latent heat equation, we can obtainThis formula shows that rs/ra and consequently SWSI relates to some meteorological variables such as net radiation Rn, the difference of temperature between soil surface and air Ts-Ta, the vapour pressure deficit eA*-eA and the airdynamic resistance ra (which can be expressed as the function of wind speed)A schematic diagram was drawn to show how the index SWSI related to meteorological variables.When net radiation Rn and vapour pressure deficit eA* e4 are given,temperature difference between soil surfaee and air Ts-Ta plays a signifficant role in SWSI estimation. Monthly SWSI at Beijing in 1980 was calculated through the schematic diagram. Although some dificulties should be overcome, feasibility of SWSI Calculation was verified to be optimistie.
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