In the last 20 years, many studies have been conducted to evaluate climate change and the hydrological processes in the arid and semi-arid regions in northwestern China. A number of studies (Chen and Xu, 2005; Chen et al., 2006; Wang et al., 2006; Shi et al., 2007) have indicated that there was a salient turning point in the hydrological and climatic processes of the region after the 1980s. This new trend was characterized by a continual increase in temperature and precipitation, added river runoff volumes, increased lake water surface elevation and area, and elevated groundwater levels. These changes have led to increased water resources, providing immediate relief to the local water shortage. However, the climate change has also caused the accelerated retreat of glaciers, which are important natural water reservoirs for the delta ecosystems in inland China. This phenomenon has raised widespread concerns worldwide and recently has become a hot topic in related academic fields.
However, it has proven difficult to achieve a thorough understanding of the nonlinear mechanism of any individual hydroclimatic process (Cannon and McKendry, 2002; Xu et al., 2008a, 2008b). Specifically, there is still a lack of effective means available to reveal the type of nonlinearity underlying hydroclimatic process. Theoretically, hydroclimatic process can be evaluated to determine if they comprise an ordered, deterministic system, an unordered, random system, or a chaotic, dynamic system, and whether change patterns of periodicity or quasi-periodicity exist. Specific to the series of climate changes that have occurred in the arid/semi-arid region of western China, such inquiries may be designed to determine if these changes represent a localized transition to a warm and wet climate type in response to global warming, or merely reflect a centennial periodicity in hydrological dynamics. To date, these questions have not received satisfactory answers; therefore, more studies are required to explore the nonlinear characteristics of hydroclimatic process from different perspectives and using different methods (Xu et al., 2009a, 2010).
For mountainous river in arid area of Northwest China, such as the Aksu River, one of headwaters of the Tarim River, which has been relatively undisturbed by human activities, is mainly recharged by rainfall, seasonal glacier melt and snowmelt, and the climate factors directly affecting the recharge of the river are temperature and precipitation. From the physical mechanism, the temperature mainly influences the runoff by glacier melt and snowmelt while precipitation supplies directly to the glaciers, snow cover, and runoff. Ahlmmann (1924) has proposed the method calculating the amount of snowmelt above the glacier equilibrium-line height using the data describing temperature; thereafter, Khodakov (1965) and Krenke (Krenke and Khodakov, 1966) further developed this approach. Kang and Ohmura (1994) also believed that the equilibrium line could be used as a standard position to estimate the amount of glacier melt. However, this approach representing an average state ignored the glacier melting intensity varying with height. Regarding the calculations for glacier melt runoff, Moore (1993) has proposed a structural model. The model divided the basin into several height zones and each zone was dealt with separately according to glacier area and non-glacial areas. The basic inputs were average temperature and precipitation of each zone with a daily time step and the outputs were runoff and evaporation of the glacier areas. But the mechanism of the model was still not well understood as it not only overlooked the infiltration of water, but also ignored the variation of parameters in space; therefore it still belonged to a lumped conceptual hydrological model. Then, there was a physics-based distributed hydrological model considering in depth about the impact on hydrological cycle from the uneven spatial distribution in watershed underlying surface (Singh and Woolhiser, 2002; Githui et al., 2009). It divided the basin into many grids and sub-basins in horizontal and layers the soil in vertical, simultaneously, and it applied some differential equations in physical and hydraulic to solve the temporal and spatial variation of runoff, according to the characteristics of runoff formation and affluxion in basin. The advantage was significant when compared to the traditional lumped conceptual hydrological model of the basin. But for the mountainous basin covered with snow and glaciers, it is still difficult to obtain extensive precise data on underlying surface by the grid method, whereas traditional statistical analysis cannot directly deal with the complicated nonlinear process of the hydroclimatic process (Xu et al., 2008b, 2009b).
For the above reasons, we neither involved complex physical mechanisms nor used traditional statistical analysis. Based on the observed climatic and hydrological data series from two hydrologic stations and four meteorological stations, this study applied several selected methods, including grey relation analysis, wavelet analysis, and regression analysis to investigate the nonlinear trends of runoff and its response to regional climate changes in the Aksu River.