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Several findings suggest that CO2 emissions in lakes are not always directly linked to changes in metabolism but can be associated with interactions with the dissolved inorganic carbon equilibrium. Alkalinity has been described as a determining factor in regulating the relative contributions of biological and inorganic processes to carbon dynamics in lakes. Here we analyzed the relationship between metabolic changes in dissolved oxygen (DO) and dissolved inorganic carbon (DIC) at different timescales in eight lakes covering a wide range in alkalinity. We used high-frequency data from automatic monitoring stations to explore the sensitivity of DIC to metabolic changes inferred from oxygen. To overcome the problem of noisy data, commonly found in high-frequency measurements datasets, we used Singular Spectrum Analysis to enhance the diel signal-to-noise ratio. Our results suggest that in most of the studied lakes, a large part of the measured variability in DO and DIC reflects non-metabolic processes. Furthermore, at low alkalinity, DIC dynamics appear to be mostly driven by aquatic metabolism, but this relationship weakens with increasing alkalinity. The observed deviations from the metabolic 1:1 stoichiometry between DO and DIC were strongly correlated with the deviations expected to occur from calcite precipitation, with a stronger correlation when accounting also for the benthic contribution of calcite precipitation. This highlights the role of calcite precipitation as an important driver of CO2 supersaturation in lakes with alkalinity above 1 meq L−1, which represents 57% of the global area of lakes and reservoirs around the world.

We use (cross) wavelet analysis to decompose the time–frequency effects of oil price changes on the macroeconomy. We argue that the relation between oil prices and industrial production is not clear-cut. There are periods and frequencies where the causality runs from one variable to the other and vice-versa, justifying some instability in the empirical evidence about the macroeconomic effects of oil price shocks. We also show that the volatility of both the inflation rate and the industrial output growth rate started to decrease in the decades of 1950 and 1960.

This article provides a fresh insight into the dynamic nexus between oil prices, the Saudi/US dollar exchange rate, inflation, and output growth rate in Saudi Arabia' economy, using novel Morlet' wavelet methods. Specifically, it implements various tools of methodology: the continuous wavelet power spectrum, the cross-wavelet power spectrum, the wavelet coherency, the multiple and the partial wavelet coherence to the annual sample period 1969-2014. Our results unveil that the relationships among the variables evolve through time and frequency. From the time-domain view, we show strong but non-homogenous linkages between the four variables. From the frequency-domain view, we uncover significant wavelet coherences and strong lead-lag relationships. From an economic view, the wavelet analysis shows that Saudi economy is still exposed to several global risk factors, which are mainly related to the oil market volatility, and the pegging of the local currency to the US dollar. Such risk factors strongly and negatively affect the real economic growth, exert more pressure on inflation, and substantially limit the freedom to pursue an independent monetary policy.

In this paper, an attempt is made to examine the relationship between inflation and stock returns in India using spectral and time-frequency methods. Scale specific relation between inflation and stock returns is unraveled, allowing us to capture the relationship at varying investment horizons. The results based on monthly data from 1994:5 to 2014:11, obtained using spectral and wavelet techniques, reveal that there exist no significant pro-cyclical interdependencies between inflation and stock returns, implying that stock returns is no longer an adequate hedge against inflation.

This study combines 8 years of middle atmospheric wind data observed at 52°N latitude from two radars in different longitudinal sectors to investigate solar tides. The power spectral density of horizontal winds exhibits a −3 power law within the frequency range 2.0 < f < 7.0 cpd (equivalent to periods 3.6 − 12.0 hr). Particularly noteworthy are the 4.8‐ and 4‐hr tides, exhibiting signal‐to‐noise ratios ranging between 13 and 16 dB, surpassing the 0.01 significance level. This challenges their previous oversight in literature, possibly due to inadequacies in prevailing noise models. Cross‐spectra between longitudinal sectors emphasize the dominance of sun‐synchronous components in the six lowest‐frequency tides. Composite spectra indicate that tidal enhancements during SSWs resemble regular seasonal variations. Intriguingly, year‐to‐year spectral variations suggest that these enhancements are more influenced by seasonal dynamics than by SSW, contrasting with established literature. These findings underscore the need to reevaluate tidal harmonics and consider appropriate noise models in future studies. Plain Language Summary Tides are ubiquitous in celestial systems, influencing celestial objects diversely when one orbits another. Extensive studies have explored the tidal effects on processes such as planetary habitability, climate fluctuations, meteorological patterns, geophysical activities, geological hazards, heat and mass circulation, and certain biological behaviors. However, most existing literature focuses on the lowest‐frequency tidal harmonics, with limited attention given to higher‐frequency ones. In the Earth's atmosphere, the exact count of solar tidal harmonics remains uncertain, and an ongoing debate persists regarding the existence of higher‐frequency harmonics, arising potentially from difficulties in distinguishing them from sporadic regional buoyancy waves. Here, we provide evidence for the statistically significant existence of the first six orders of tidal harmonics, extracted from 8 years of middle atmospheric wind observations. Spectral coherence between two distinct longitudinal sectors signifies that the six harmonics primarily correspond to sun‐synchronous tides synchronized with the Sun. The presence of higher‐frequency tides suggests that tidal effects are characterized by greater complexity than currently understood. Key Points Wind spectrum reveals 6 tidal harmonics significantly higher than background noise with −3 frequency power law Coherence between two longitudinal sectors reveals that the harmonics are synchronized with the Sun Winter tidal enhancements seem to be influenced by seasonal factors rather than SSW, presenting a contrast to existing literature

This study assesses the relationships between vegetation dynamics and climatic variations in Pakistan from 2000 to 2023. Employing high-resolution Landsat data for Normalized Difference Vegetation Index (NDVI) assessments, integrated with climate variables from CHIRPS and ERA5 datasets, our approach leverages Google Earth Engine (GEE) for efficient processing. It combines statistical methodologies, including linear regression, Mann–Kendall trend tests, Sen's slope estimator, partial correlation, and cross wavelet transform analyses. The findings highlight significant spatial and temporal variations in NDVI, with an annual increase averaging 0.00197 per year (p < 0.0001). This positive trend is coupled with an increase in precipitation by 0.4801 mm/year (p = 0.0016). In contrast, our analysis recorded a slight decrease in temperature (− 0.01011 °C/year, p < 0.05) and a reduction in solar radiation (− 0.27526 W/m 2 /year, p < 0.05). Notably, cross-wavelet transform analysis underscored significant coherence between NDVI and climatic factors, revealing periods of synchronized fluctuations and distinct lagged relationships. This analysis particularly highlighted precipitation as a primary driver of vegetation growth, illustrating its crucial impact across various Pakistani regions. Moreover, the analysis revealed distinct seasonal patterns, indicating that vegetation health is most responsive during the monsoon season, correlating strongly with peaks in seasonal precipitation. Our investigation has revealed Pakistan's complex association between vegetation health and climatic factors, which varies across different regions. Through cross-wavelet analysis, we have identified distinct coherence and phase relationships that highlight the critical influence of climatic drivers on vegetation patterns. These insights are crucial for developing regional climate adaptation strategies and informing sustainable agricultural and environmental management practices in the face of ongoing climatic changes.

Under the background of climate warming, drought events occur frequently. Generally, meteorological drought leads to agricultural drought. Understanding the spatiotemporal distribution, characteristics of drought and the relationship between meteorological and agricultural drought are important for early drought warning. Northeast China (NEC) was selected as the study area. The spatiotemporal characteristics of meteorological drought and agricultural drought in different seasons in NEC were analyzed. Correlation analysis was employed to analyze the relationship between meteorological and agricultural drought in different vegetation types. Furthermore, cross-wavelet analysis was employed to further analyze the relationship between meteorological drought and agricultural drought, explore the teleconnection and large-scale climate patterns and investigate possible causes of drought variations in this region. The results showed that (1) the frequency of mild meteorological drought and low and that of moderate agricultural drought was high; (2) there was a significant positive correlation between meteorological drought and agricultural drought, while the change in agricultural drought lagged behind that of meteorological drought. (3) A strong correlation between meteorological drought and agricultural drought was identified in cropland areas. (4) The El Niño Southern Oscillation and Pacific interannual oscillation were important factors affecting the changes in meteorological drought and agricultural drought NEC. The results provide scientific ground for the sustainable development of agriculture, drought monitoring and early warning, disaster prevention and mitigation in NEC.

Synthetic aperture radar interferometry (InSAR) has proven to be a powerful tool for monitoring landslide movements with a wide spatial and temporal coverage. Interpreting landslide displacement time-series derived from InSAR techniques is a major challenge for understanding relationships between triggering factors and slope displacements. In this study, we propose the use of various wavelet tools, namely, continuous wavelet transform (CWT), cross wavelet transform (XWT) and wavelet coherence (WTC) for interpreting InSAR time-series information for a landslide. CWT enables time-series records to be analysed in time-frequency space, with the aim of identifying localized intermittent periodicities. Similarly, XWT and WTC help identify the common power and relative phase between two time-series records in time-frequency space, respectively. Statistically significant coherence and confidence levels against red noise (also known as brown noise or random walk noise) can be calculated. Taking the Huangtupo landslide (China) as an example, we demonstrate the capabilities of these tools for interpreting InSAR time-series information. The results show the Huangtupo slope is affected by an annual displacement periodicity controlled by rainfall and reservoir water level. Reservoir water level, which is completely regulated by the dam activity, is mainly in ‘anti-phase’ with natural rainfall, due to flood control in the Three Gorges Project. The seasonal displacements of the Huangtupo landslide is found to be ‘in-phase’ with respect to reservoir water level and the rainfall towards the front edge of the slope and to rainfall at the higher rear of the slope away from the reservoir.

This research is the earliest attempt to understand the impact of inflation and the interest rate on output growth in the context of Pakistan using the wavelet transformation approach. For this study, we used monthly data on inflation, the interest rate, and industrial production from January 1991 to May 2020. The COVID-19 pandemic has affected economies around the world, especially in view of the measures taken by governmental authorities regarding enforced lockdowns and social distancing. Traditional studies empirically explored the relationship between these important macroeconomic variables only for the short run and long run. Firstly, we employed the autoregressive distributed lag (ARDL) cointegration test and two causality tests (Granger causality and Toda-Yamamoto) to check the cointegration properties and causal relationship among these variables, respectively. After confirming the long-run causality from the ARDL bound test, we decomposed the time series of growth, inflation, and the interest rate into different time scales using wavelet analysis which allows us to study the relationship among variables for the very short run, medium run, long run, and very long run. The continuous wavelet transform (CWT), the cross-wavelet transform (XWT), cross-wavelet coherence (WTC), and multi-scale Granger causality tests were used to investigate the co-movement and nature of the causality between inflation and growth and the interest rate and growth. The results of the wavelet and multi-scale Granger causality tests show that the causal relationship between these variables is not the same across all time horizons; rather, it is unidirectional in the short-run and medium-run but bi-directional in the long-run. Therefore, this study suggests that the central bank should try to maintain inflation and the interest rate at a low level in the short run and medium run instead of putting too much pressure on these variables in the long-run.

The advent of climate change has induced frequent occurrence of droughts in the past few decades. Identification of hydrological droughts require computation of drought indices by probabilistic standardization procedures. The existing hydrological drought indices could not answer the zero monthly streamflow condition for the ephemeral streams. This issue was resolved by developing a modified Standardized Streamflow Index to characterize the hydrological drought of Upper Kangsabati River Basin, West Bengal, India. 45 hydrological droughts were extracted for the basin and the most severe drought occurred in the year 2015–2016. The basin experienced the most severe drought of 10.67 severity and longest drought duration of 13 months. A bivariate analysis of drought characteristics was carried out using copula technique to determine different design drought events. The bivariate distribution which showed the basin experienced most severe drought of 16 years and longest duration drought of 15 years ‘OR’ return period. Propagation time of the drought hazard from the meteorological to the hydrological drought is extensively studied in this research using both correlation and Cross Wavelet Transform (XWT) methods. XWT was mostly used for qualitative comparison of hydrological and meteorological signal in drought propagation studies in the past. In this research, a novel quantitative approach of using XWT and the phase angles obtained between the hydrological and meteorological signals is proposed to determine the drought propagation times. It was concluded that the basin had in general a drought propagation time of 2 months. However, there were seasonal variability in the drought propagation times showing prompt response in the summer season which increased to 2 months for monsoons and stretching far to 5 months for the late winter.