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Rainfall–runoff processes appear to be highly nonlinear in Bayinbluk watersheds of the northwestern China. In this study, the time-scale wavelet transform has been used for the analysis of this nonstationary system. The Haar and Morlet wavelet transform were used to analyse the rainfall–runoff conversion relationship. Wavelet power spectrum and change point methods are also employed to analyse rainfall rates and runoffs measured at daily to half-hourly sampling rate. The four experimental sites (Luoto, Haer, Kuce and Shengl) are located in the Tianshan Mountains (Xinjiang province, China). Correlation analysis and wavelet transform are first applied to runoff process in different underlying surfaces. Wavelet analyses of rainfall rates and runoffs also give meaningful information on the temporal variability of the rainfall–runoff relationship. Change point and wavelet power spectrum analysis provide simple interpretation of energy distribution between different scales. The results indicate that wavelet transform is a good method for analysing the nonlinear relationship of temporal–spatial responses between rainfall and runoff. This method allowed quantification of the processes affecting runoff and provided an insight into their implications in surface water management. Copyright © 2011 John Wiley & Sons, Ltd.

Rotated principal component analysis (PC) was performed on monthly Aerosol Optical Depth (AOD) from Moderate Resolution Imaging Spectroradiometer (MODIS) data over East Asia for the period of March 2000–January 2006. The first PC mode is a south–north dipole with a strong positive loading between 30–35°N and 130–150°E over middle latitude East Asia and a weaker negative loading in southern parts over East Asia. The first PC mode explains 32.44% of the total variance. By analysing time series of the PC1-3, results show the PC-1 and PC-3 modes are important and both have distinct changes from the period 2000–2003 to 2004–2006; the former pattern (in middle latitudes over East Asia) is characterized in a decreasing linear trend and the latter (in eastern China) is in an increasing linear trend in the full 71 month evolution. Furthermore, based on the wavelet power spectrum analysis, it is found that the distinct changes of the monthly AOD in middle latitudes over East Asia (the PC-1 pattern) are connected to the multi-scale variations at intra-seasonal (3–6 month) and annual (12 month) scales. While calculating the correlation of the PC-1 with wind fields at 850 hPa from the NCEP/NCAR reanalysis dataset, it is shown that the PC-1 is closely related to the U and V (horizontal) components over subtropical East Asia and western north Pacific, which well represents East Asian monsoon features. Finally, by comparing the PC-1 pattern in May between 2003 and 2004, results show that the higher (lower) AOD in 2003 (2004) is associated with weaker (stronger) U component at 850 hPa in middle latitudes over East Asia. Copyright © 2008 Royal Meteorological Society

Wavelet analysis is a powerful tool with which to analyse the hydrologic effects of dam construction and operation on river systems. Using continuous records of instantaneous discharge from the Lees Ferry gauging station and records of daily mean discharge from upstream tributaries, we conducted wavelet analyses of the hydrologic structure of the Colorado River in Grand Canyon. The wavelet power spectrum (WPS) of daily mean discharge provided a highly compressed and integrative picture of the post-dam elimination of pronounced annual and sub-annual flow features. The WPS of the continuous record showed the influence of diurnal and weekly power generation cycles, shifts in discharge management, and the 1996 experimental flood in the post-dam period. Normalization of the WPS by local wavelet spectra revealed the fine structure of modulation in discharge scale and amplitude and provides an extremely efficient tool with which to assess the relationships among hydrologic cycles and ecological and geomorphic systems. We extended our analysis to sections of the Snake River and showed how wavelet analysis can be used as a data mining technique. The wavelet approach is an especially promising tool with which to assess dam operation in less well-studied regions and to evaluate management attempts to reconstruct desired flow characteristics. Copyright © 2005 John Wiley & Sons, Ltd.

This paper studied the spatial and temporal variability of the statistical structures of precipitation across Xinjiang, China, by analysing the time series of daily precipitation from 50 weather stations during the period from 1961 to 2008. Three indices precipitation concentration index (CI), precipitation concentration degree (PCD) and precipitation concentration period (PCP) were used to detect precipitation concentrations and the associated spatial patterns. The results show that higher precipitation CI values were mainly observed in Southern Xinjiang, whereas lower precipitation CI values were mostly detected in Northern Xinjiang. The precipitation CI values are noticeably larger in places where both annual total precipitation and number of rainy days are lower. The Mann–Kendall trend test demonstrates that the most parts of Xinjiang are characterized by no significant trends of precipitation CI at the 0.05 significance level. The periodicity characteristic of precipitation CI time series in Xinjiang could be detected by wavelet power spectrum analysis, and significant periods of that in most of Xinjiang were concentrated on 2–5 years band. The results of PCP reveal that rainfall in Xinjiang mostly occurs in summer, and the rainy season arrives earlier in Eastern Xinjiang than Western Xinjiang, whereas the results of PCD indicate that the rainfall in Northern Xinjiang was more dispersed within a year than that in Southern Xinjiang. Copyright © 2010 Royal Meteorological Society

Rainfall characteristics at different temporal resolutions play a significant role in sustainable urban water management. In this study we attempted to identify the temporal characteristics and variability of point rainfall measured in Melbourne, Australia. Statistical moments, lag1 autocorrelation, the Buishand's Q test for homogeneity, the Mann–Kendall (MK) test for trend and wavelet analyses for temporal variability were carried out for rainfall intensities at resolutions of 0.1, 0.5, 1, 3, 6, 12 h and for the monthly rainfall depths and proportion dry ratios. Series of rainfall intensities at different temporal scales and the monthly rainfall depths and proportion dry ratios were accumulated from the high resolution rainfall dataset for the period from 1925 to 2002. Homogeneity of rainfall intensity was found to increase as the temporal scale increases. Both rainfall intensities and monthly rainfall depths were found to be serially correlated. The 2nd, 3rd and 4th statistical moments of rainfall intensities increased as the resolution increased. While no statistically significant trends were found using the MK test, there were indications that trends are more likely as the temporal scale increases. Wavelet power spectra identified a dominant frequency scale (0.25–1 year) in the 3, 6 and 12 h rainfall intensities that were periodically observed in a 5 to 10–year cyclic order. This phenomenon could be influenced by the inter-annual variability of the El Nino Southern Oscillation (ENSO). Copyright © 2009 Royal Meteorological Society