The hydrological cycle in a typical RAA is characterized by the processes that river water disperses and is evaporated during dispersion. Water bodies such as rivers, reservoirs and lakes are the main water source of oasis because of little precipitation and intense potential evaporation. A typical RAA and the associated hydrological processes are shown in Fig.2, together with the estimated annual water budget for an oasis in the Tarim Basin (Tang, 2003): around 86% of annual evapotranspiration originate from streamflow through river bed seepage and water diversion, the remaining 14% comes from the rainfall which is stored in the dry soil.
The main water dispersive processes from river include i) saturated riverside and river spreading in downstream plain area, which are natural processes; ii) water is diverted into irrigation area by canal and consumed among the fields, which are manmade processes; iii) because of the large intake into irrigation area, the water table depth in irrigation area is usually more shallow than surrounding environment and consequently induce groundwater flow to non-irrigation area, in addition, part of surface drainage is dispersed to surrounding environment, which are the processes that are interposed by both nature and human activities.
Water is dispersed from the river and consumed surrounding the river, and the evapotranspiration is the final consumption of runoff in a typical RAA. The runoff is evapotranspired back to the atmosphere through various land surfaces. The main water consumptive processes include i) water is evaporated from water surface such as riverway, reservoir and lake; ii) water is evapotranspired in irrigation area; iii) water is evapotranspired in non-irrigation area. According to the landscape variability, evapotranspiration in non-irrigation area can be specified by wild land, sandy wasteland and wetland etc.
A runoff-evaporation (RE) land surface hydrological model, which will be introduced in this paper, was carried out by Hu et al. (2004) and Tang et al. (2004) to model the runoff-evaporation processes in arid plain oasis. The complete model consists of a channel network sub-model and several sub-models of different land use unit (which is similar to HRU, hydrological response unit,(Flügel and Cooley, 1995)) that incorporate the lateral and vertical components identified above. The development of each component of runoff-evaporation processes is introduced in more detail below, and the overall structure is shown in Fig.3.
A channel system is used to represent both natural and manmade lateral dispersive processes. Fig.4 shows a schematic representation of a typical hydrological concept where the natural and manmade dispersive processes occur within a river basin in hyper-arid area. The natural dispersive processes (saturated channel side and channel spreading; represented by dark shaded areas in Fig.4) generally occur adjacent to channels, while manmade dispersive processes (irrigation, represented by the shaded areas with solidus in Fig.4) occur in irrigation area.
According to the mass conservation in the channel system, the governing equation of dispersive processes is used as follows:
where, Ci[M3] is channel inflow from upstream, Cd[M3] is net water diversion between upstream and downstream, Ce[M3] is evaporation from open channel water surface, Cg[M3] is infiltration, Co[M3] is channel outflow to downstream, and Cs[M3] is channel storage. The channel loss (Ce + Cg) and channel flow is assumed to be in direct proportion for simplicity. If the channel is riverway, the river loss is estimated from the averaged stream flow as follow: where, 5#5 is the proportionality constant derived from historical observation. And river evaporation is estimated from pan evaporation and river water surface area. For the case of canal, the canal loss is in direct proportion to the inflow (i.e. abstraction volume) as follow: where, 8#8 is canal penetration coefficient, 9#9 is canal utility factor, describing the relationship between canal abstraction volume and resulting water arrived at the field. Canal utility factors highly depend on liner type and management level and should be identified by field experiments for each level canal. To get the canal utility factor, the canals in irrigation area are classified to four levels: trunk canal, branch canal, lateral canal and field canal. The canal utility factor 9#9 is given by: where, the argument i refers to the canal class index, 13#13[1/KM] is the loss fate of the canal class from field experiments, li[KM] is the length of the canal class. One part of canal loss is arbitrarily considered to recharge groundwater with a canal penetration coefficient (8#8) because the water table in irrigation area is very shallow, and the remaining part is considered to evaporate back to atmosphere from the canal water surface and the adjacent saturated area. The canal seepage coefficient highly depends on underlying soil, water table depth, and vegetation nearby the canal, further research should be done to investigate the canal penetration. A calibrated canal seepage coefficient of 0.8 is used in this study. For the case of drainage, a method modified from the DRAIN package of MODFLOW (McDonald and Harbaugh, 1988) is used to estimate drainage from irrigation area. The drainage can be calculated as: where, 16#16[1/T] is drainage coefficient, describing water table decrease ratio due to head difference between water table and drainage level in a lumped way, Ad[M2] is the drainage area, h[M] is the phreatic level and hd[M] is drainage bottom level. The drainage coefficient highly depends on underlying soil conductivity and the interspace between offtakes. It is a regionalized parameter which represents the drainage system state. The hydrological response of the irrigation area and non-irrigation area is much different because of human disturbance. The irrigation area and land use units in non-irrigation area are separately modeled, i.e. groundwater budgets of irrigation area and non-irrigation area are separately calculated and there is groundwater exchange between them in each time step. The groundwater exchange X between irrigation area and non-irrigation area can be calculated using: where, 18#18[1/T] is groundwater exchange coefficient, describing water table decrease ratio due to water head difference between irrigation area and non-irrigation area in a lumped way, hn[M] is phreatic level of non-irrigation area, and Ad[M2] is the irrigation area. The parameter groundwater exchange coefficient should be specified by calibrating the model. The groundwater level is then calculated from the water store change in the groundwater reservoir: where, 21#21 is specific yield, Qlg is water infiltration from soil layer, and Ep is evaporation from phreatic water. Qlg and Ep will be decided in the vertical processes of the model. The reproduced groundwater depth is compared with observed groundwater depth for validation of the model.The vertical processes characterize the subsurface as consisting of two soil layers in unsaturated zone and one groundwater layer. The surface is described by N land cover types, where n = 1 represents irrigation area, and n = 2, 3,¡, N represents N - 1 different types of land cover in non-irrigation area. The irrigation area is described by M crop cover types, where m = 1, 2,¡, M represents M different types of crop cover. There is no restriction on the number of land cover and crop types, but N and M will almost always be less than 10 for simplicity or because of shortage of data. It is worth mentioning that the fraction of land cover is time dependence because of land surface transformation. The model construction is shown schematically in Fig.5. The evapotranspiration from each land cover is characterized by potential evapotranspiration, together with crop factor and soil moisture stress. Associated with each land cover class is an upper soil layer (soil layer 1), lower soil layer (soil layer 2) and groundwater layer. The upper layer (soil layer 1) is designed to represent the behavior of thin topsoil, and the lower layer (soil layer 2) is used to characterize the soil moisture behavior of the root zone. The upper layer, where water can be evaporated without soil moisture stress, responds to irrigation (I[MM]), rainfall (P[MM]) and atmospheric forcing to evaporation. The lower layer responds to not only irrigation and rainfall when the upper layer is wetted but also the remaining atmospheric forcing to evaporation and capillarity (Ep[MM], phreatic evaporation). For the wetland class, there is only the groundwater layer and the evaporation is calculated from the potential evaporation. In the present version of model, the soil characteristic (these are the distribution of specific water yield and parameters for phreatic evaporation, as described below) are the same for all land cover classes. However, irrigation area and land use units in non-irrigation area may have different soil moisture and water table distribution in each time step. Infiltrations from upper and lower soil layer, drainage from groundwater are computed for irrigation area and land use units in non-irrigation area. It is worth mentioning that there are no surface or subsurface runoff items because the rainfall-runoff processes are not dominating in typical RAA.
The evaporation from upper soil layer and lower soil layer are considered in the model. The atmospheric forcing to evaporation (i.e., evapotranspiration ability, Ea[n]) is specified as:
In equation 8, the argument n refers to the land cover class index. Throughout the remainder of the paper, the dependence of land cover class is implied by n and the dependence of crop cover class is implied by m even if not noted specifically. Kc[n] is the crop factor, ET0[MM] is the reference evapotranspiration based on the FAO Penman-Monteith method. The integrative crop factor over the irrigation area is computed as the sum of crop cover classes weighted by the respective area fractions: where Cc[m] is the fraction of crop cover for the mth (m = 1, 2,¡, M) crop cover class of irrigation area and 23#23Cc[m] = 1. There is no soil moisture stress for the upper soil layer, i.e., all the water in the upper soil layer is available to supply the atmospheric demand. The evaporation from lower soil layer is considered when there is insufficient water in upper layer to supply the atmospheric demand in one time step. In this case, the evaporation from the lower layer, El[n], is: In equation 10, Ks[n] is a soil moisture stress factor on the water availability in the root zone for the nth land cover class and Er[n] is the remaining evaporation ability. The soil moisture stress factor is expressed as: where Wl[n] is the soil moisture content in lower layer and WL is the soil storage capability of the lower layer. If the lower layer is not wetted, i.e. Wl[n] < WL, there is evaporation from phreatic water, Ep, to the lower layer. It is given by where Eg is the phreatic evaporation ability. Based on the formulation of Mao et al. (1997); Mao et al. (1999) and Zhao et al. (2000), phreatic evaporation ability is estimated as: where, E0[MM] is water surface evaporation, H[n][M] is the water table depth, 5#5,31#31,32#32 are empirical parameters, R[n][M] is root depth.The upper layer infiltration Qul and lower layer infiltration Qlg is computed when the soil is wetted, i.e., there are infiltration when irrigation and precipitation, which is added to soil moisture storage at the end of the previous time step, exceeds the storage capacity of the soil. The infiltration to groundwater will raise water table therefore drain or spread through groundwater exchange.