Primary hydrological modeling only involved in the development of concepts, theories and models of individual components of the hydrological cycle, such as overland flow (Keulegan, 1944; Horton, 1939), channel flow (Freeze and Harlan, 1969), infiltration (Horton, 1933; Green and Ampt, 1911), evaporation (Richardson, 1931; Penman, 1948), interception (Horton, 1919), subsurface flow (Hursh and Brater, 1941) and base flow (Hewlett, 1961aa; Hewlett, 1961ab) until the middle of the 1960s. Thereafter the decades of the 1960s witnessed the digital revolution that made possible the integration of models of different components of the hydrological cycle and simulation of virtually the entire watershed (Singh and Woolhiser, 2002). A proliferation of watershed hydrology models ranging from simple empirical models with a lumped model structure to physically based, complicated and spatially distributed models were developed, e.g. Stanford Watershed Model (Crawford and Linsley, 1966), Antecedent Precipitation Index Model (Sittner et al., 1969), Tank model (Sugawara, 1967), Xinanjiang model (Zhao et al., 1980; Zhao, 1992), TOPMODEL (Beven and Kirkby, 1979), Systeme Hydrologique Europeen (Abbott et al., 1986b; Abbott et al., 1986a) etc. These watershed models, as assemblages of mathematical descriptions of components of the hydrological cycle, are well known and in current use. Since there are many components of hydrological cycle, limited components can be integrated to avoid overcomplicated and over parameterization. The model structure and hydrological cycle components are mainly determined by the purpose for which the model is built and the boundary condition characteristics of model applied area such as climate, topography, vegetation and land use. For example, a hydrological model for flood control is quite different from the one for water resources management. Likewise, a model for a tropical rainy climate zone is significantly different from the one for a tundra climate zone. Existing hydrological models significantly emphasize describing precipitation to streamflow processes such as overland flow, subsurface flow, base flow and channel flow. Some models even use hillslope as the basic element to represent valley and the runoff formation (Ambroise et al., 1996a; Ambroise et al., 1996b; Yang et al., 1998; Yang and Musiake, 2003; Beven and Kirkby, 1979; Robinson et al., 1995). The rainfall to runoff processes are commonly assumed as the dominating hydrological response and the abstractions such as evapotranspiration, depression storage and detention storage are treated as subordination. A prevailing way is to group hydrological component processes into vertical and lateral processes (Becker and Braun, 1999; Becker and Nemec, 1987). Vertical fluxes are related to processes such as infiltration, percolation and evapotranspiration. Lateral fluxes occur by redistribution processes of surface runoff, water in the saturated and unsaturated soil zone or in the groundwater flowing roughly parallel to the terrain surface. Many studies of vertical fluxes lead to the development of techniques for separation of overland flow, subsurface flow, and base flow (Scherrer and Naef, 2003) and are widely used in hydrological models. The Hortonian mechanism, subsurface flow mechanism, and partial source area contributions are then recognized as contributors to runoff and concentrate into the stream through a linear or nonlinear system (Dooge, 1959; Nash, 1957; Lighthill and Whitham, 1955). The runoff redistribution processes such as surface water infiltration, channel loss and surface evaporation are truly considerable before the surface water reaches the outlet of watershed, but few approaches incorporate them. The two sophisticated assumptions are widely applied along with the development of hydrological modeling: rainfall-runoff processes are dominating processes and redistribution of runoff is negligible. The following items might be the reasons why the two assumptions were made. (i) Hydrology was originally defined as the science that attempts to answer the question, 'What happens to the rain?'(Penman, 1961) Attentions are naturally concentrated on precipitation and runoff. (ii) Rainfall-runoff processes are dominating hydrological processes after intense precipitation, especially in humid mountainous area. (iii) For the general hydrological modeling whose purpose is flood control, hydropower generation or reservoir operation, quantification of streamflow generated from event precipitation is very important. For the models with the purpose of water resources management, investigation on rainfall-runoff processes lead to the understanding on how surface water resources are generated. (iv) Redistribution of runoff, especially human induced abstraction, is hard to be represented in a general way in hydrological model. Furthermore, redistribution processes are usually concealed in the parameterized rainfall-runoff mechanism in a lumped model.
Consequently, most hydrological models are designed for humid area where rainfall-runoff processes are dominating. And the spatially distributed runoff is directly accumulated because the redistribution of runoff is neglected, that might cause miscalculation of discharge and is recognized as a scale issue. As further research process-oriented simulation of hydrological processes is done, researchers found redistributions of runoff such as runoff routing and groundwater-surface water interactions gain increasing importance with increasing catchment area (Uhlenbrook et al., 2004). The runoff redistribution is more obvious in semi-arid area where rainfall-runoff processes might not be the dominating hydrological processes. Bromley et al. (1997) described the surface hydrology in south-west Niger and reported that generated runoff moves to be intercepted and is directed as quickly as possible to vegetated area for evapotranspiration. Peugeot et al. (1997) investigated runoff generation processes at the East Central Supersite of the HAPEX-Sahel experiment and concluded that seepage leads to the abstraction of non negligible volumes of water and discontinuities occur in the surface water transmission within a catena. Güntner and Bronstert (2004) considered the lateral redistribution of surface runoff between adjacent landscape patches is an important process in semi-arid area and incorporated the redistribution into hydrological modeling by using an areal fraction parameter. Such studies in semi-arid area show the limitation of the assumption, which is widely acquiescent in process-oriented hydrological modeling, that the rainfall-runoff transmission is dominating processes and continuous. Some physical ecological studies have also shown that unit runoff is decreasing with increasing size of catchments as a result of local infiltration and storage and the connectivity of runoff-generating and runoff-absorbing area is important at all scale levels. Outcomes of research on geomorphology shows the connectivity is dominated by both the rainfall magnitude-frequency-duration characteristics and physically and biological controlled thresholds (Cammeraat, 2002). Water budget approaches offer the possibility to shun parts of the problem mentioned before and are usually used in semi-arid area long term modeling. Flerchinger et al. (1998) and Flerchinger and Cooley (2000) compared a uniform with an aggregated water balance and calculated a ten-year water balance of a semi-arid watershed in southwest Idaho, USA. The results show that evapotranspiration is nearly 90% of effective precipitation. Some meteorological researches even derive "negative runoff" based on estimations of precipitation minus evaporation because rainfall produce little runoff and large amounts of water are extracted from the river for irrigation in some semi-arid area (Dettinger and Diaz, 2000; Martin et al., 1999). This suggests that rainfall-runoff processes might not be the dominating processes and more attention should be paid to runoff-evaporation processes in semi-arid area.
In order to represent runoff-evaporation process, two key questions can be formulated. (i) How much, where and when does water vaporize? The temporal and spatial distribution of evapotranspiration represents a key role of the hydrological cycle in semi-arid area. Evapotranspiration is thought an important component of the complete hydrological cycle apart from runoff generation but is always simply simulated in hydrological modeling because it is not possible to directly verify the modeled spatial evapotranspiration patterns with high temporal resolution (Mo et al., 2004; Strasser and Mauser, 2001). (ii) What does the evaporated water originate from? Evaporated water often comes from precipitation resided in soil water and groundwater. But the surface water supply and horizontal groundwater recharge might also be important source, especially in semi-arid irrigated area.
In this paper, we concentrate our attention on runoff-evaporation processes and try to systematically describe water dispersion and consumption in a semi-arid area. We introduce a runoff-evaporation (RE) hydrological model which was designed to representing runoff-evaporation processes and employ it in an endoreic river basin of central Asia. Before introduction of the model, we begin with a discussion about the dominating hydrological processes in river basin scale in Section 2. Components of runoff-evaporation processes are delineated and the RE model is introduced in Section 3. In Section 4, we give a model application employed in an endoreic catchment in central Asia. The paper closes with discussion and conclusion in Section 5.