The combination of wavelet analysis methods with data-driven models is a prevalent approach to conducting hydrological time series forecasting, but the results are affected by the accuracy of the wavelet decomposition of the series. The choice of decomposition level is one of the key factors for the wavelet decomposition. In this paper, the data of daily precipitation and streamflow time series measured in the upper reach of the Heihe River Basin in Northwest China were used as an example, and the influence of the decomposition level on wavelet-based hydrological time series forecasting was investigated. The true components of the precipitation series were identified, and the modeling results using 10 decomposition levels and two decomposition types were compared. The results affirmed that the wavelet-based modeling performance is sensitive to the choice of decomposition level, which is determined by the time series analyzed, but has no relation with the decomposition type used. The essence of the choice of decomposition level is to reveal the complex variability of hydrological time series under multi-temporal scales, and first knowing the true components of series could guide the choice of decomposition level. Through this study, the relationship among original series’ characteristics, the choice of decomposition level, and the accuracy of wavelet-based hydrological time series forecasting can be more clearly understood, and it can be an improvement for wavelet-based data-driven modeling.

A changing climate has been posing significant impacts on vegetation growth, especially in the Yellow River Basin (YRB) where agriculture and ecosystems are extremely vulnerable. In this study, the data for normalized difference vegetation index (NDVI) obtained from moderate-resolution imaging spectroradiometer (MODIS) sensors and climate data (precipitation and temperature) derived from the national meteorological stations were employed to examine the spatiotemporal differences in vegetation growth and its reaction to climate changes in the YRB from 2000–2019, using several sophisticated statistical methods. The results showed that both NDVI and climatic variables exhibited overall increasing trends during this period, and positive correlations at different significant levels were found between temperature/precipitation and NDVI. Furthermore, NDVI in spring had the strongest response to temperature/precipitation, and the correlation coefficient of NDVI with temperature and precipitation was 0.485 and 0.726, respectively. However, an opposite situation was detected in autumn (September to November) since NDVIs exhibited the weakest responses to temperatures/precipitation, and the NDVI’s correlation with both temperature and precipitation was 0.13. This indicated that, compared to other seasons, increasing the temperature and precipitation has the most significant effect on NDVI in spring (March to May). Except for a few places in the northern, southern, and southwestern regions of the YRB, NDVI was positively correlated with precipitation in most areas. There was an inverse relationship between NDVI and temperature in most parts of the central YRB, especially in summer (June to August) and growing season (May to September); however, there was a positive correlation in most areas of the YRB in spring. Finally, continuous attention must be given to the influence of other factors in the YRB.