STOCHASTIC ANALYSIS AND MODELING OF HYDROLOGIC AND CLIMATOLOGIC TIME SERIES

G PADMANABHAN, Purdue University

Abstract

Two important aspects in the area of stochastic model construction--spectral analysis and causal connection between time series--are investigated in this study. The conventional methods of spectral analysis currently used in hydrology and climatology suffer from several drawbacks and their power of resolution is poor. Therefore, four recently developed methods--Maximum Entropy, Maximum Likelihood, Non-Integer and G-spectral methods are investigated in this study and compared with conventional method by using hydrologic climatologic data. Maximum Entropy (ME) method easily emerges to be superior to other methods and hence is recommended for use in hydrology and climatology. Some of the stochastic model identification tools which can be easily computed as a part of general computational scheme of ME method make it useful in stochastic model construction. This feature of the method has been demonstrated in this study. Hitherto, spectral analysis and model construction have been traditionally looked upon as two separate aspects in hydrology. However, Maximum Entropy method makes it possible to integrate these two aspects. Other features such as its close relationship with Maximum Likelihood method and its adaptability for cross spectral estimation have been demonstrated in this study as additional advantages of ME method. One of the problems associated with ME method is the determination of the correct order of the filter to be used in the method. A criterion developed by Kashyap for this purpose has been investigated and recommended to be used with ME method. In general the parametric approach to spectral analysis in which ARMA type models are used require objective criteria to determine the order of ARMA models. Various criteria for order determination proposed in the literature have been investigated in the present study with a view to use them in spectral estimation using parametric approach. Based on the statistical properties of the decision criteria, Kashyap's criterion is recommended for AR models. It is the only criterion which gives the probability of error in choosing the order. However, the only presently available practical criterion for ARMA models in Akaike's AIC. Investigation of causality is important in constructing better forecasting models for effect variables. Solar activity has been widely hypothesized as a mechanism influencing hydrologic and climatologic processes. However, statistical evidence in establishing causal connections between them have often been contradictory. Traditionally cross correlation methods have been used to infer causal connections. However, interpretation of significance of cross correlation coefficients of autocorrelated series such as those encountered in this study is difficult. Therefore, the individual series between which the causal connections are sought to be inferred are reduced to white residual series. The cross correlations between these whitened series are used to draw inference about causal connections between the original series. The results indicate weak but statistically significant correlation. The lags at which cross correlation is significant vary for different series. However, the lags at which cross correlations are significant can be used in developing univariate models with exogeneous terms or bivariate models and these can be tested for their forecasting capability. In order to investigate the often hypothesized 22-year cycle in droughts and speculations about its connection with the Hale cycle of Solar activity, a detailed analysis of Palmer's drought index series was undertaken. 14 to 20-year cycles were identified by using high resolution spectral analysis methods. It has been demonstrated that simple AR models can preserve the long term oscillations in the drought indices.

Degree

Ph.D.

Subject Area

Hydrology

COinS