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Indian Institute of Science (2001)

Structural Analysis And Forecasting Of Annual Rainfall Series In India

Sreenivasan, K R

Titre : Structural Analysis And Forecasting Of Annual Rainfall Series In India

Auteur : Sreenivasan, K R

Etablissement de soutenance : Indian Institute of Science

Grade : PhD 2001

Résumé partiel
The objective of the present study is to forecast annual rainfall taking into account the periodicities and structure of the stochastic component. This study has six Chapters. Chapter 1 presents introduction to the problem and objectives of the study. Chapter 2 consists of review of literature. Chapter 3 deals with the model formulation and development. Chapter 4 gives an account of the application of the model. Chapter 5 presents results and discussions. Chapter 6 gives the conclusions drawn from the study. In this thesis the following model formulations are presented in order to achieve the objective. Fourier analysis model is used to identify periodicities that are present in the rainfall series.1 These periodic components are used to obtain discrotized ranges which is an essential input for the Fourier series model. Auto power regression model is developed for estimation of rainfall and hence to compute the first order residuals errlt The parameters of the model are estimated using genetic algorithm. The auto power regression model is of the form, ( Refer the PDF File for Formula) where αi and βi are parameters and M indicates modular value. Fourier series model is formulated and solved through genetic algorithm to estimate the parameters amplitude R, phase Φ and periodic frequency wj for the residual series errlt. The ranges for the parameters R, Φ and wj were obtained from Fourier analysis model. errl’t= /µerrlt+ Σj Rcos(wjt+ Φ) Further, an integrated auto power regression and Fourier series model developed (with parameters of the model being known from the above analysis) to estimate new rainfall series Zesťt=Zµ Σ t αi(ZMi-t ) βi+µerrl+ Σj Rcos(wjt+ Φ) and the second order residuals, err2t is computed using, err2t = (zt –Zesťt) Thus, the periodicities are removed in the errlt series and the second order residuals err’2f obtained represents the stochastic component of the actual rainfall series. Auto regressive model is formulated to study the structure of the stochastic component err2t. The auto regressive model of order two AR(2) is found to fit well. The parameters of the AR(2) model were estimated using method of least squares. An exponential weighting function is developed to compute the weight considering weight as a function of AR2) parameters. The product of weight and Gaussian white noise N(0, óerr2) is termed as weighted stochastic component. Also, drought analysis is performed considering annual (January to December) and summer monsoon (June to September) rainfall totals, to determine average drought interval (idrt) which is used in assigning signs to the random component of the forecasting model. In the final form of the forecasting model. Zest”t = Z µ Σ t αi(ZMi-t ) βi+µerrl+ Σj Rcos(wjt+ Φ) ± WT(Φ1, Φ2)N(0, óerr2) The weighted stochastic component is added or subtracted considering two criteria. Criterion I is used for all rainfall series except all-India series for which criterion II is used. The criteria also consider average drought interval Further, it can be seen that a ± sign is introduced to add or subtract the weighted stochastic component, albeit the stochastic component itself can either be positive or negative.

Présentation (ETD IISC)

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