Rescaled range analysis and conditional probability-based probe into the intrinsic pattern of rainfall over North Mountainous India

In work reported here, we have explored rainfall over North Mountainous India for pre-monsoon (MAM), Indian summer monsoon (JJAS), post-monsoon (OND) and Annual. The dependence of JJAS on MAM and OND on JJAS has been explored through conditional probabilities utilizing frequency distribution. An autocorrelation structure has shown that a low lag-1 autocorrelation coefficient characterizes all the time series. We have implemented rescaled range analysis. Through Hurst's exponent and fractal dimension, we have observed that the MAM time series of rainfall over North Mountainous India has a smooth trend and low volatility. We have further observed that for MAM and JJAS, we have , and D is closer to 1 than to 2. However, we have further observed that for OND and Annual rainfall over North Mountainous India and . Therefore, these two time series have been characterized by high volatility and randomness.

Viscoelasticity and Noise Properties Reveal the Formation of Biomemory in Cells

Living cells are neither perfectly elastic nor liquid and return a viscoelastic response to external stimuli. Nanoindentation provides force distance curves allowing the investigation of cell mechanical properties, and yet, these curves can differ from point to point on cell surface revealing its inhomogeneous character. In the present work, we propose a mathematical method to estimate both viscoelastic and noise properties of cells, as these are depicted on the values of the scaling exponents of relaxation function and power spectral density respectively. The method uses as input the time derivative of the response force in a nanoindentation experiment. Generalized moments method and/or rescaled range analysis are used to study the resulting time series depending on their non-stationary or stationary nature. We conducted experiments in living Ulocladium Chartarum spores. We found that spores, in the approaching phase present a viscoelastic behavior with the corresponding scaling exponent in the range 0.25-0.52, and in the retracting phase present a liquid-like behavior with exponents in the range 0.67-0.85. This substantial difference of the scaling exponents in the two phases suggests the formation of biomemory as response of the spores to the indenting AFM mechanical stimulus. The retracting phase may be described as a process driven by bluish noises, while the approaching one is driven by persistent noise.

Long Memory in Earthquake Time Series: The Case Study of the Geysers Geothermal Field

The present study aims at proving the existence of long memory (or long-range dependence) in the earthquake process through the analysis of time series of induced seismicity. Specifically, we apply alternative statistical techniques borrowed from econometrics to the seismic catalog of The Geysers geothermal field (California), the world’s largest geothermal field. The choice of the study area is essentially guided by the completeness of the seismic catalog at smaller magnitudes (a drawback of conventional catalogs of natural seismicity). Contrary to previous studies, where the long-memory property was examined by using non-parametric approaches (e.g., rescaled range analysis), we assume a fractional integration model for which the degree of memory is defined by a real parameter d, which is related to the best known Hurst exponent. In particular, long-memory behavior is observed for d > 0. We estimate and test the value of d (i.e., the hypothesis of long memory) by applying parametric, semi-parametric, and non-parametric approaches to time series describing the daily number of earthquakes and the logarithm of the (total) seismic moment released per day. Attention is also paid to examining the sensitivity of the results to the uncertainty in the completeness magnitude of the catalog, and to investigating to what extent temporal fluctuations in seismic activity induced by injection operations affect the value of d. Temporal variations in the values of d are analyzed together with those of the b-value of the Gutenberg and Richter law. Our results indicate strong evidence of long memory, with d mostly constrained between 0 and 0.5. We observe that the value of d tends to decrease with increasing the magnitude completeness threshold, and therefore appears to be influenced by the number of information in the chain of intervening related events. Moreover, we find a moderate but significant negative correlation between d and the b-value. A negative, albeit weaker correlation is found between d and the fluid injection, as well as between d and the annual number of earthquakes.

Evolution of meteorological factors during 1980–2015 in the Daqing River Basin, North China

Precipitation and temperature data, such as the homogeneity, trend, abrupt change, and periodicity, obtained at 40 meteorological stations in the Daqing River Basin from 1980 to 2015 are analyzed using the Mann–Kendall method, anomaly accumulation, Rescaled range analysis (R/S analysis) and wavelet transform. The regularity of climate change is studied to provide guidelines for the rational utilization of water resources. The results show that the annual precipitation has an insignificant upward trend and suddenly changes in 2007. The precipitation evolution can be divided into three types of periodicity, that is, 22–32, 8–16, and 3–7 year time scales, where the 28 year scale is the first main period of precipitation change. The annual average temperature shows a notable upward trend, with 1992 as the change year. The annual average temperature can be divided into three types of periodicity, that is, the 25–32, 14–20, and 5–10 year time scales, where the 28 year scale is the first main period of temperature change. In conclusion, the climate of the Daqing River Basin gradually turns into humid and hot climate. The results provide valuable reference for the assessment of the effects of climate change, and the management of water resources.

Analysis of Long-term Variability through Temperature and Humidity Data in Urban Meteorological Observation Network

<p>In the process of producing grid data using observation data, the density of the stations were found to have the greatest influence on spatial (Hwang and Ham, 2013). Currently, the resolution of Korea’s ground detection network is about 12 to 15km additional stations need to be set up to improve spatial accuracy. However, indiscriminate installation of observatories is an objective challenge because of the enormous cost and the various factors to consider. It is important to select major observation points on an objective basis based on the existing KMA (Korea Meteorological Administration)'s AWS(Automatic Weather System), ASOS(Automated Synoptic Observing System)  data to increase the representative and reliability of the observation data. However, the establishment of an observatory so far has been chosen for subjective observation purposes, which may make it difficult to derive scientific data. In this study there is identified the long-term variability of urban meteorological data using the Hurst exponent (H) obtained through Rescaled range analysis (R/S analysis). And additional observation points are proposed for each meteorological element through network analysis.</p><p>R/S analysis is an analysis that measures the variability of time series by standardizing observations over time to make them in a dimensionless ratio and analyze the changes according to the length of the data used. H between 0 and 1 provides a criterion for distinguishing the measure of correlation that a time series has. H = 0.5 means that the present event does not affect subsequently, however the other values are correlated, not independent, and continuum of influence (Hwang and Cha 2004). The meteorological factors data were obtained from SK planet, AWS, ASOS installed in Seoul. As a result, long-term relativity between temperature and humidity are shown to be at a minimum of 0.750 and a maximum of 0.941.</p><p>Key words :  R/S analysis, Hurst exponent, long-term relativity</p>