Non-stationary time series (TS) analysis has gained an explosive interest over the recent decades in different applied sciences. In fact, several decomposition methods were developed in order to extract various components (e.g., seasonal, trend and abrupt components) from the non-stationary TS, which allows for an improved interpretation of the temporal variability. The wavelet transform (WT) has been successfully applied over an extraordinary range of fields in order to decompose the non-stationary TS into time-frequency domain. For this reason, the WT method is briefly introduced and reviewed in this paper. In addition, this latter includes different research and applications of the WT to non-stationary TS in seven different applied sciences fields, namely the geo-sciences and geophysics, remote sensing in vegetation analysis, engineering, hydrology, finance, medicine, and other fields, such as ecology, renewable energy, chemistry and history. Finally, five challenges and future works, such as the selection of the type of wavelet, selection of the adequate mother wavelet, selection of the scale, the combination between wavelet transform and machine learning algorithm and the interpretation of the obtained components, are also discussed.

Urban flooding has become a serious issue in most Chinese cities due to rapid urbanization and extreme weather, as evidenced by severe events in Beijing (2012), Ningbo (2013), Guangzhou (2015), Wuhan (2016), Shenzhen (2019), and Chongqing (2020). The Chinese “Sponge City Program” (SCP), initiated in 2013 and adopted by 30 pilot cities, is developing solutions to manage urban flood risk, purify stormwater, and provide water storage opportunities for future usage. Emerging challenges to the continued implementation of Sponge Cities include (1) uncertainty regarding future hydrological conditions related to climate change projections, which complicates urban planning and designing infrastructure that will be fit for purpose over its intended operating life, and (2) the competing priorities of stakeholders and their reluctance to make trade-offs, which obstruct future investment in the SCP. Nature-Based Solutions (NBS) is an umbrella concept that emerged from Europe, which encourages the holistic idea of considering wider options that combine “Blue–Green” practices with traditional engineering to deliver “integrated systems of Blue–Green–Grey infrastructure”. NBS includes interventions making use of natural processes and ecosystem services for functional purposes, and this could help to improve current pilot SCP practices. This manuscript reviews the development of the SCP, focusing on its construction and design aspects, and discusses how approaches using NBS could be included in the SCP to tackle not only urban water challenges but also a wide range of social and environmental challenges, including human health, pollution (via nutrients, metals, sediments, plastics, etc.), flood risk, and biodiversity.

The Palmer Drought Severity Index (PDSI) can lead to controversial results in assessing droughts responding to global warming. Here we assess recent changes in the droughts over China (1961–2013) using the PDSI with two different estimates, i.e., the Thornthwaite ( PDSI_th ) and Penman‐Monteith ( PDSI_pm ) approaches. We found that droughts have become more severe in the PDSI_th but slightly lessened in the PDSI_pm estimate. To quantify and interpret the different responses in the PDSI_th and PDSI_pm , we designed numerical experiments and found that drying trend of the PDSI_th responding to the warming alone is 3.4 times higher than that of the PDSI_pm , and the latter was further compensated by decreases in wind speed and solar radiation causing the slightly wetting in the PDSI_pm . Interestingly, we found that interbasin difference in the PDSI_th and PDSI_pm responses to the warming alone tends to be larger in warmer basins, exponentially depending on mean temperature.