Probabilistic Formulation of Spatio-temporal Drought Pattern

Summary Meteorological and hydrological drought occurrences along time and space take place randomly and therefore their scientific quantifications are possible by the probabilistic methods. Herein drought occurrences are assumed to have spatial and temporal stationarity with underlying independent generating mechanism. The drought stricken area is considered as composed of mutually exclusive and collectively exhaustive subareas each with different probability of drought occurrence. Two types of spatio-temporal drought formulations are presented. The first is referred to as the regional persistence model and it assumes that if any subarea is stricken by drougth it will remain to stay in this state till the whole area is covered by drought. The second alternative is multi-seasonal model and it is based on the assumption that drought stricken area might recover and have wet period during the course of time. The necessary theoretical probability distribution functions for partially drought stricken areas are derived based on the Bernoulli trials both along time and space axis. The expectation and variance parameters are derived based on the percentage of drought stricken area and the basic wet and dry spell probabilities. Necessary charts for practical purposes are prepared and interpretations are given. Received January 23, 1998 Revised June 30, 1998     

Stochastic Modeling of the Van Lake Monthly Level Fluctuations in Turkey

Summary  Planning, design, construction and operation of lakeshore structures require information about the future likely extremes of the lake levels at a given risk percentage. Alternative future likely synthetic sequences can be numerically generated provided that the underlying generating mechanism of the lake level fluctuation phenomenon is identified. Simple linear and periodic nonlinear models are used for modeling the deterministic part in the lake level records. Linear trend is eliminated from the original lake level historic data by regression line technique. The nonlinear part needs two stages for its identification. First Fourier series is applied to model interannual periodicities in the lake level fluctuation series and then monthly standardization procedure is applied for seasonal periodic nonlinear component modeling. A second order Markov model is found suitable for the remaining stochastic parts. The application of the methodology is presented for the Lake Van monthly level data in eastern Turkey. Suitable models are identified and their parameters are estimated for trend, periodic and stochastic parts. Likely, synthetic lake levels are generated by the stochastic model and hence lake level extreme values are depicted for the next 2, 6, 12, 24, 60 and 120 months with risk calculations. Such risk calculations take into account the stochastic characteristics of the lake level fluctuations only. The deterministic parts as linear trends and periodicities are added to the stochastic extreme events for the actual simulation of the lake levels. The model presented in this paper is not for time prediction of future lake levels but rather for the simulation of possible equally likely extreme lake level value occurrences over any desired future period. Received April 22, 1998/Revised July 28, 1999