## 1. Introduction

[2] One of the challenges in hydrology is to predict the effect of land-use changes, such as clearing and afforestation, on the partitioning of precipitation into evapotranspiration and runoff. It has been long recognized that evapotranspiration is the result of complex interactions between the atmosphere, soil, and vegetation [*Brutsaert*, 1982]. Although the processes by which vegetation affects hydrological response of a catchment have been well documented, it has been difficult to develop models that can be used to make predictions at the catchment scales. This is partly because of the lack of understanding about the interactions and feedbacks among the processes and limited available data. It is almost inevitable that for such a model to be of practical use it has to be simple and based on measurable properties of the catchment. Despite the complex processes and interactions that are associated with evapotranspiration, it has long been assumed that available energy and water are the primary factors determining the rate of evapotranspiration [*Budyko*, 1958].

[3] A number of simple models for estimating mean annual evapotranspiration have been developed based on the above assumption with various degrees of empiricism [*Schreiber*, 1904; *Budyko*, 1958; *Pike*, 1964]. However, these models do not consider the effect of catchment characteristics on evapotranspiration. *Choudhury* [1999] generalized these relationships by introducing an adjustable parameter. Recently, *Zhang et al.* [2001] developed a similar model with a parameter assumed to be controlled by soil water storage. A common feature of these models is to assume that evapotranspiration is a known function of precipitation and available energy (as measured by potential evapotranspiration). Although the functional forms of these equations differ, their numerical values are similar. In these models, mean annual evapotranspiration generally approaches precipitation in regions where potential evapotranspiration greatly exceeds the precipitation, and conversely, mean annual evapotranspiration approaches potential evapotranspiration where precipitation is significantly greater than potential evapotranspiration. However, these studies offered no scientific basis as to why a particular function was chosen apart from the fact that it respects the above physical limits.

[4] *Milly* [1994] developed a mathematical framework for mean annual evapotranspiration that provides insights into these relationships. The model is based on the hypothesis that the long-term evapotranspiration is determined by the local interaction of precipitation and potential evapotranspiration, mediated by soil water storage. With his theoretical framework, he identified several key variables believed to be responsible for the partitioning of precipitation into evapotranspiration and runoff. Although simple in concept, the practical application of this model is limited because of the complex numerical solutions required.

[5] In 1981, B. P. Fu, from Nanjing University, China, published a paper on relationships between long-term evapotranspiration and precipitation [*Fu*, 1981]. He combined dimensional analysis with mathematical reasoning and developed analytical solutions for mean annual evapotranspiration. The relationships represented by his model are very similar to those known as Budyko's curve. The paper was published in Chinese only, and 20 years later the work is still relatively unknown outside China.

[6] This paper aims to contribute to the understanding of the effects of climatic and catchment characteristics on the partitioning of mean annual precipitation into evapotranspiration. We will revisit the work of *Fu* [1981] and use this to gain some insight into the key catchment properties controlling the partitioning. The data used in the analysis cover wide ranges of climate, vegetation, and other catchment characteristics. The results therefore are expected to be generally applicable to catchments in most geographic zones.