CHAPTER I
INTRODUCTION
1.1
Background
At present, stochastic modelling of seasonal hydrological time series is an
accepted approach for data generation and forecasting of hydrological events. Although
almost from the beginning of the century the importance of statistical approaches for
analysing hydrological data was evident, it was not until the mid 1950’s that formal
development of stochastic modelling started with the introduction and application of
autoregressive models for monthly rainfall (Hannan, 1955). Since then, extensive
research efforts have been towards improving the early concepts and models, providing
physical (conceptual) justification of some models, introducing alternative models and
developing and applying improved estimation procedures as fitness tests for such
models.
About thirty-five years has elapsed since Hannan first suggested the lag-one auto
regressive model for the modelling and simulation of monthly rainfall. Since then
significant steps in this area are represented by the works of Thomas and Fiering (1962)
for modelling annual and seasonal streamflows, Yevjevich (1963) and Roesner and
Yevjevich (1966) for modelling annual runoff and monthly precipitation and
streamflow, respectively; Matalas (1967) for multivariate lag-one autoregressive
modelling and Yevjevich (1972a) for extending the lag-one autoregressive models to
multilag with seasonal parameters. About the same time, the book of Box and Jenkins
(1970) stirred interest in the application of a new class of models, namely the
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autoregressive-moving average (ARMA) models which have gained wide application in
stochastic hydrology (Carlson et al., 1970; O’Connell, 1971; McKerchar and Delleur,
1973; Hipel et al., 1977; Lettenmaier and Burges, 1977; Curry and Bras, 1978; Salas et
al., 1980; Cooper and Wood, 1980; Rao et al., 1982; and Stedinger and Taylor, 1982). A
landmark in the modelling of seasonal hydrology time series was the development of the
disaggregation model (Valancia and Schaake, 1973), which allows the generation of
seasonal hydrological samples by preserving statistics at both annual and seasonal time
scales. Improvements and applications of disaggreregation models have also been made
(see for instance, Mejia and Rousselle, 1974; Todini, 1980; Lane, 1982; Santos and
Salas, 1983; Valencia et al., 1983 and Stedinger aand Vogel, 1984).
Synthetic hydrology is an accepted practice for the planning and management of
the water resources systems. This study will focus in simulation of rainfall. Depending
on the particular system considered either seasonal or annual synthetic rainfall might be
required. Stochastic simulation of water resources times series in general and
hydrologic time series in particular has been widely for several decades for various
problems related to planning and management of water resources systems (Salas et al,
1980; Loucks et al, 1981).
Stochastic simulation of hydrologic time series such as rainfall is typically based
on mathematic models. For this purpose a number of stochastic models have been
suggested in literature (Salas, 1993; Hipel and Mcleod, 1994). The solution from many
hydrological problems is intimately related to a better knowledge of the rainfall process
such as the development of reliable streamflow and groundwater models, the prediction
of floods and droughts, the design of the data collection networks among others.
In this study, the disaggregation methods were used to generate accurate
synthetic rainfall data to predict the accurate runoff. In general, all three disaggregation
models satisfactorily preserve annual and seasonal (monthly) rainfall generation.
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1.2
Statement of Problems
Stoshastic data generation aims to provide alternative hydrologic data sequences
that are likely to occur in future. These data sequences, particularly monthly time series
are widely used in water resources planning and operation studies to assess the reliability
of alternative system designs and policies and to understand the variability in future
system performances (Loucks et al., 1981). However, for valid and realistic results is
necessary that these synthetic monthly data sequences should preserve both monthly and
annual statistical parameters of historical data especially mean, variance, correlation and
skewness. As monthly data generation models such as the Thomas-Feiring model
(Thomas and Feiring, 1962) rarely produce monthly data sequences that preserve both
monthly and annual parameters of the historical record, disaggregation models are
currently being widely used to generate such data sequences. Disaggregation models
produce monthly data sequences by disaggregation annual data that have been generated
by suitable annual data generation model.
The purpose of rainfall generation is to generate accurate, reliable synthetic
rainfall data for predict accurate runoff from this generation. Disaggregation method is
uses to preserve the statistical characteristics such as mean, standard deviation, skewness
and season to season correlation.
This study will prove that synthetic rainfall generation can obtained a good
model. These models can preserve the statistical characteristic of historical data because
synthetic runoff generation not easily preserved the statistical characteristic. This
problem happened with many reasons such as infrastructure that build at river basin,
economic and etc. In this study, the problem will solve when the rainfall generation
applied.
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1.3
Objectives
In general, this study focuses the stochastic simulation of rainfall time series for
seasonal data. The objectives of this study are;
1. To apply the disaggregation models in the rainfall simulation.
2. To evaluate the model performance in the rainfall simulation.
3. To identify the best model in the rainfall simulation.
1.4
Scope
The study covers the application disaggregation methods. Those methods
composed of basic model (Valencia and Schaake, 1973); extended model (Mejia and
Rousselle, 1973) and the condensed model (Lane, 1979; Grygier and Stedinger, 1991).
The data obtained from the JPS Hydrology and Water Resources Division, one of
division in Department of Irrigation and Drainage of Malaysia (DID). The utility of this
approach is to demonstrate through the application of mean monthly rainfall from 5 sites
in Johor measured in millimetre (mm). The data modelled were the data rainfall for 52
years from 1949 until 2000.
The study uses the disaggregation method to the monthly (seasonal) and annual
rainfall data for single site multi season case.