scholarly journals Measuring and restructuring the risk in forecasting drought classes: an application of weighted Markov chain based model for standardised precipitation evapotranspiration index (SPEI) at one-month time scale

2020 ◽  
Vol 72 (1) ◽  
pp. 1-10
Author(s):  
Zulfiqar Ali ◽  
Ijaz Hussain ◽  
Amna Nazeer ◽  
Muhammad Faisal ◽  
Muhammad Ismail ◽  
...  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Zulfiqar Ali ◽  
Ijaz Hussain ◽  
Muhammad Faisal ◽  
Ibrahim M. Almanjahie ◽  
Muhammad Ismail ◽  
...  

Drought is a complex stochastic natural hazard caused by prolonged shortage of rainfall. Several environmental factors are involved in determining drought classes at the specific monitoring station. Therefore, efficient sequence processing techniques are required to explore and predict the periodic information about the various episodes of drought classes. In this study, we proposed a new weighting scheme to predict the probability of various drought classes under Weighted Markov Chain (WMC) model. We provide a standardized scheme of weights for ordinal sequences of drought classifications by normalizing squared weighted Cohen Kappa. Illustrations of the proposed scheme are given by including temporal ordinal data on drought classes determined by the standardized precipitation temperature index (SPTI). Experimental results show that the proposed weighting scheme for WMC model is sufficiently flexible to address actual changes in drought classifications by restructuring the transient behavior of a Markov chain. In summary, this paper proposes a new weighting scheme to improve the accuracy of the WMC, specifically in the field of hydrology.


2011 ◽  
Vol 52 (4) ◽  
pp. 372-390
Author(s):  
DUNG TIEN NGUYEN ◽  
XUERONG MAO ◽  
G. YIN ◽  
CHENGGUI YUAN

AbstractThis paper considers singular systems that involve both continuous dynamics and discrete events with the coefficients being modulated by a continuous-time Markov chain. The underlying systems have two distinct characteristics. First, the systems are singular, that is, characterized by a singular coefficient matrix. Second, the Markov chain of the modulating force has a large state space. We focus on stability of such hybrid singular systems. To carry out the analysis, we use a two-time-scale formulation, which is based on the rationale that, in a large-scale system, not all components or subsystems change at the same speed. To highlight the different rates of variation, we introduce a small parameter ε>0. Under suitable conditions, the system has a limit. We then use a perturbed Lyapunov function argument to show that if the limit system is stable then so is the original system in a suitable sense for ε small enough. This result presents a perspective on reduction of complexity from a stability point of view.


2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jie Liu ◽  
Xingquan Ji ◽  
Kejun Li ◽  
Kaiyuan Zhang

A multi-time scale optimal dispatch model based on the scenario method and model predictive control (MPC) in the AC/DC distribution network is established due to the uncertainty of wind and load. A Markov chain dynamic scenario method is proposed, which generates scenarios by characterizing the forecast error via empirical distribution. Considering the time correlation of the forecast error, Markov chain is adopted in the Markov chain dynamic method to simulate the uncertainty and variability in wind and load with time. A multi-time scale optimal dispatch strategy based on MPC is proposed. The operation scheduling of operation units is solved in day-ahead and intraday optimal dispatch by minimizing the expected value of total cost in each scenario. In the real-time optimal dispatch, the stability and robustness of system operation are considered. MPC is adopted in the real-time optimal dispatch, taking the intraday scheduling as reference and using the roll optimization method to compute real-time optimal dispatch scheduling to smooth the output power. The simulation results in a 50-node system with uncontrollable distributed energy demonstrate that the proposed model and strategy can effectively eliminate fluctuations in wind and load in AC/DC distribution networks.


2021 ◽  
Author(s):  
Peyman Mahmoudi ◽  
Allahbakhsh Rigi

Abstract The main objective of this study was to predict the transition probability of different drought classes by applying Homogenous and non- Homogenous Markov chain models. The daily precipitation data of 40 synoptic stations in Iran, for a period of 35 years (1983–2018), was used to access the study objectives. The Effective Drought Index (EDI) was applied to categorize Iran’s droughts. With the implementation of cluster analysis on the daily values of effective drought index (EDI), it was observed that Iran can be divided into five separate regions based on the behavior of the time series of the studied stations. The spatial mean of the effective drought index (EDI) of each region was also calculated. After forming the transition frequency matrix, the dependent and correlated test of data was conducted via chi-square test. The results of this test confirmed the assumption that the various drought classes are correlated in five studied regions. Eventually, after adjusting the transition probability matrix for the studied regions, the homogenous and non-homogenous Markov chains were modeled and Markov characteristics of droughts were extracted including various class probabilities of drought severity, the average expected residence time in each drought class, the expected first passage time from various classes of droughts to the wet classes, and the short-term prediction of various drought classes. Regarding these climate areas, the results showed that the probability of each category is reduced as the severity of drought increases from poor drought category to severe and very severe drought. In the non-homogeneous Markov chain, the probability of each category of drought for winter, spring, and fall indicated that the probability of weak drought category is more than other categories. Since the obtained anticipating results are dependent on the early months, they were more accurate than those of the homogeneous Markov chain. In general, both Markov chains showed favorable results that can be very useful for water resource planners.


2000 ◽  
Vol 179 ◽  
pp. 205-208
Author(s):  
Pavel Ambrož ◽  
Alfred Schroll

AbstractPrecise measurements of heliographic position of solar filaments were used for determination of the proper motion of solar filaments on the time-scale of days. The filaments have a tendency to make a shaking or waving of the external structure and to make a general movement of whole filament body, coinciding with the transport of the magnetic flux in the photosphere. The velocity scatter of individual measured points is about one order higher than the accuracy of measurements.


1984 ◽  
Vol 75 ◽  
pp. 599-602
Author(s):  
T.V. Johnson ◽  
G.E. Morfill ◽  
E. Grun

A number of lines of evidence suggest that the particles making up the E-ring are small, on the order of a few microns or less in size (Terrile and Tokunaga, 1980, BAAS; Pang et al., 1982 Saturn meeting; Tucson, AZ). This suggests that a variety of electromagnetic and plasma affects may be important in considering the history of such particles. We have shown (Morfill et al., 1982, J. Geophys. Res., in press) that plasma drags forces from the corotating plasma will rapidly evolve E-ring particle orbits to increasing distance from Saturn until a point is reached where radiation drag forces acting to decrease orbital radius balance this outward acceleration. This occurs at approximately Rhea's orbit, although the exact value is subject to many uncertainties. The time scale for plasma drag to move particles from Enceladus' orbit to the outer E-ring is ~104yr. A variety of effects also act to remove particles, primarily sputtering by both high energy charged particles (Cheng et al., 1982, J. Geophys. Res., in press) and corotating plasma (Morfill et al., 1982). The time scale for sputtering away one micron particles is also short, 102 - 10 yrs. Thus the detailed particle density profile in the E-ring is set by a competition between orbit evolution and particle removal. The high density region near Enceladus' orbit may result from the sputtering yeild of corotating ions being less than unity at this radius (e.g. Eviatar et al., 1982, Saturn meeting). In any case, an active source of E-ring material is required if the feature is not very ephemeral - Enceladus itself, with its geologically recent surface, appears still to be the best candidate for the ultimate source of E-ring material.


2019 ◽  
Vol 62 (3) ◽  
pp. 577-586 ◽  
Author(s):  
Garnett P. McMillan ◽  
John B. Cannon

Purpose This article presents a basic exploration of Bayesian inference to inform researchers unfamiliar to this type of analysis of the many advantages this readily available approach provides. Method First, we demonstrate the development of Bayes' theorem, the cornerstone of Bayesian statistics, into an iterative process of updating priors. Working with a few assumptions, including normalcy and conjugacy of prior distribution, we express how one would calculate the posterior distribution using the prior distribution and the likelihood of the parameter. Next, we move to an example in auditory research by considering the effect of sound therapy for reducing the perceived loudness of tinnitus. In this case, as well as most real-world settings, we turn to Markov chain simulations because the assumptions allowing for easy calculations no longer hold. Using Markov chain Monte Carlo methods, we can illustrate several analysis solutions given by a straightforward Bayesian approach. Conclusion Bayesian methods are widely applicable and can help scientists overcome analysis problems, including how to include existing information, run interim analysis, achieve consensus through measurement, and, most importantly, interpret results correctly. Supplemental Material https://doi.org/10.23641/asha.7822592


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