Propagation of Different Stochastic Frameworks for Modeling, Forecasting and Spatial Analysis of Drought Hazard

Abstract

This thesis develops various stochastic strategies and provides amalgamations of various data-driven techniques in uni variate, multivariate and spatio-temporal settings. Some important applications from the eld of hydrology are provided. These applications are purely related the e ective use of uni-variate and multi- variate time series data particularly for drought management and hydrological process control. Due to global warming, the risk of drought has been increased in several regions of the world. Therefore, continuous monitoring, prediction, and spatial characterization of drought from precise and accurate procedures play very important role for e ective drought mitigation policies. In this per- spective, this thesis presents seven major proposals which cover continuous mon- itoring, forecasting and spatial characterization of drought hazards. In uni vari- ate setting, this thesis proposed one drought index: the Probabilistic Weighted Joint Aggregative Drought Index (PWJADI), and a new weighting scheme for weighted Markov chain model. Both of these methods are carried out with their applications on various meteorological stations of Pakistan. Outcomes associ- ated with this research show that the proposed methods can e ectively handle uni-variate time series data for drought monitoring and short-term prediction. In multivariate setting, we proposed three frameworks under spatial and regional settings. First framework is purely application based where we considered the problem of multi-scaling characteristics and the choice of best time scale for regional monitoring of drought. In this work, we investigated appropriate time scale of Standardized Precipitation Temperature Index (SPTI) Ali et al. (2017a) drought index using geo-reference points of meteorological stations. In the sec-ond work, we developed a novel regionalized drought monitoring framework which requires minimal drought monitoring stations by clustering meteorological stations. Here, we introduced transition probability matrix based k-mean proce- dure for the identi cation of homogenous drought characterization regions. Our results lead towards minimal use of resources. The third framework presents a novel way to accumulate decisions of important time scales, where the transition probabilities of drought classes were used as a weight for each time scale. Here, we supported our rationale by including the investigations which are our key results in the two preceding frameworks. Our results suggest that, the proposed framework can be e ectively used for e cient and accurate drought monitoring. In further study, we introduce a novel ensemble procedure for the comparison of drought indices. Here, we proposed a new framework: the Drought Inten- sity Pattern Determinate (DIPD) by developing and con guring a new index of drought pattern recognition-the Drought Concentration Index (DCI). Appli- cation of the proposed procedure is provided by incorporating three drought indices and fty two meteorological stations of Pakistan. Our results indicate that, the proposed procedure is exible to de ne pattern of drought severity and able to compare drought indices under regional setting. In addition, we in- troduced a new generalized non-parametric framework for handling uncertainty associated with extreme events. Numerical and graphical ndings of this study show that the use of only one distribution has a greater risk of inaccurate re- porting of extreme events. Moreover, non-optimization of several probability distributions may create a chaotic situation for general drought practitioners. However, to reduce the error for accurate reporting of extreme events, probabil-ity plotting position formulas are good candidates. Finally, the study suggests improvements in the time series data of rainfall before its deployments in the statistical model. In this regards, we propagate a new drought index named: the Precision Weighted Standardized Precipitation Index (PWSDI). Outcomes associated with this part of the research show that improve time series data are good candidates for modeling and monitoring hydrological drought with more precision under regional settings.