CHAPTER II
LITERATURE REVIEW
2.1
Introduction
The generations of synthetic series are generally needed for reservoir sizing, for
determining the risk of failure (or reliability) of water supply for irrigation system, for
determining the risk of f
ailure of dependable capacities of hydroelectric systems, for
planning studies of future reservoir operation and similar applications (Salas et al.,
1980). In the river basin studies the stochastic sequences of inflows and rainfall are used
to determine h
ow different system designs and operating policies might perform (Loucks
et al., 1981). The methods of synthetic data generation have various techniques to be
tested. Therefore the study of reservoir operation system can employ various
alternatives stoch
astic hydrologic time series models to evaluate different scenario of
water resources system operation.
Since the rainfall and inflows are the important inputs to the water resources
system, the development of good stochastic models is essential in orde
r to determine an
optimal system operation. The appropriate models that generate flow sequences are that
the models manage to characterize the rainfall ideally represents all the statistical and the
correlation structure of the corresponding observed rain
falls.
6
2.2
Time Series
A time series is a set of observations that are arranged chronologically. In time
series analysis, the order of occurrences of observations is crucial. There are two
aspects to the study of time series
–
analysis and modelling. T
he aim of analysis is to
summarise the properties of a time series and to characterise its salient features. This
may be done either in the time domain or in frequency domain. In the time domain
attention is focused on the frequency domain it is cyclical
movements which are studied.
The two forms of analysis are complementary rather than competitive. The same
information is processed in different ways, thereby giving insights into the nature of the
time series. The main reason for modelling a time seri
es is to enable forecasts of future
values to be made. Forecasts are then made by extrapolation.
2.2.1
Reviews in Time Series Analysis
A great of data in business, economics, engineering and the natural sciences
occur in the form of the time series where
observations are dependent. Box and Jenkins
(1976) defined that the technique available for the analysis of such series of dependent
observations is called time series analysis. Kottegoda (1980) was defined that the time
series is a set of observations t
hat measure the variation in time of some aspect of a
phenomenon, such as the rate of flow in a river, the water level in a lake, the dissolved
oxygen in a stream or the sediment load in a channel.
Time series analysis also defined as the procedure of fi
tting a time series or
stochastic model to the time for use in application. The objective is to make inferences
regarding the basic features of the stochastic process from the information captained in
the time series. Stochastic model is usually develope
d based on the available data at
hand, aimed at reproducing the inherent statistical properties observed in the data.
7
Laws of chance govern majority of hydrology phenomena in nature. The terms,
chance, random, probabilistic and stochastic are considered
synonyms when refer to
phenomena subject to the laws of chance (Yevjevich, 1972). Hence the probabilistic
series is also called stochastic process. A mathematical model representing a stochastic
model or time series model (Salas et al., 1980). It has a
certain mathematical form or
structure and asset of parameters. Stochastic process is strictly stationary if its
probability distribution is invariant to shifts in time and is second order stationary when
the first two moments of the probability distribu
tion of the process are invariant to time
shift. The second order stationarity is a widely used concept in hydrologic time series is
transformed so as to obey the normal probability law.
Time series modelling is a process that can be simple series on
the type of model
to use and on the selection techniques are much simpler. However, there are various
techniques available and some techniques are more complex than others. Hence the
simplicity or complexity of the modelling process ultimately depends on
the modeller.
Testing goodness of fit of the model the data and also but not necessarily, to produce
likely future sequences or to forecast events over a short period of time (Kottegoda,
1980). The application of time series analysis is recognized as th
e practical use in
dealing with modelling of hydrologic time series and water resources system.
Natural hydrological processes are either stochastic or combined determination
stochastic processes. Pure deterministic processes with negligible stochasti
c variation
can e realized only under controlled, artificial conditions. Generally, they are a
combination of various deterministic and stochastic processes (Yevjevich, 1972). In the
real circumstance the inflow and rainfall processes consisting of the s
easonal variability.
Hence it is appropriate that the generation of synthetic rainfall sequences to be
represented by the stochastic models. The well

known models used in the generation of
the synthetic rainfall series are disaggregation and periodic aut
oregressive and/or
moving average models. In this study the discussion only focus in disaggregation
model. These models should preserve all properties of the observed data. However, this
cannot be achieved and criteria for evaluating the statistical res
emblance between
8
historic and generated hydrology data have to be chosen (Ledolter, 1978). It is often
desired to generate hydrologic time series, which preserve the statistical properties at
more than one time level (for example, annual and seasonal). F
or instance, generated
monthly inflows must reproduce the basic statistics (e.g., mean, standard deviation,
skewness coefficient and coefficient correlation) of observed monthly flow data.
Further, they should represent adequately the historic characteris
tics at annual levels.
Hydrologists have constructed time

series
models
for the daily, monthly, annual
and other time intervals for the simulation studies of a water

resource system. The
mathematical operations involved in attaining the monthly hydrolog
ic data from the
daily hydrologic data and the annual hydrologic data from either the daily or the
monthly hydrologic data are standard and well known. Through the utilization of these
operations one can find the covariance and the spectral relations amon
g the hydrologic
sequences corresponding to different sampling intervals. Once these relations are
known, the hydrologist, starting from the smallest interval, can calculate the covariance
and the spectral structures of the hydrologic sequences correspond
ing to larger sampling
intervals. One can then construct the time

series
models
corresponding to these larger
intervals from the theoretically calculated covariance and spectral density functions
without ever constructing the data for larger intervals or
without the computation of the
sample covariance and the sample spectral

density functions for larger intervals. This
paper establishes the relationships between the covariances and between the spectra,
respectively, of the hydrologic time series with tim
e steps which are multiples of each
other, such as daily, monthly and annual intervals. The stochastic structure in the time
domain of the series with the longer time steps can be derived in terms of the structure of
the series with the shorter time steps
. An aggregation scheme and describes, in detail,
the filters and the many

to

one transformations that are required to go from the smaller
to larger time sampling intervals. The relations show that when the hydrologic time

series
models
are disaggregated
from larger to smaller time sampling intervals the
transformations involved are one

to

many, indicating that there are many ways for the
disaggregation
whereas there is only one unique way for aggregation (
Kavvas et al.,
1976).
9
A pure statistic models are
developed using the records of previous inflows
series. Meanwhile the combine deterministic

stochastic model is combination between
the deterministic rainfall

runoff model and the stochastic rainfall model.
2.3
Disaggregation
2.3.1
Introduction
Stochastic
models that simultaneously treat a time series at several time scales
have become popular for both research and practical applications. Disaggregation is
stochastic generation that starts with a previously generated aggregate series and
subdivides or disa
ggregates that series into a finer scale time series. Disaggregation
modelling has proven to be a very practical approach, especially for multi site and
multivariate analysis.
Disaggregation methods have recently become a major technique for modelling
h
ydrologic time series. In the disaggregation approach, the seasonal series is
disaggregated from the annual series which is generated by an annual model fitted to the
annual data. These solution techniques are attractive for generating multi season
strea
mflow sequences for a single site or for several sites (Valencia and Schaake, 1973;
Meija and Rousselle, 1976; Tao and Delluer, 1976; Todini, 1980).
Disaggregation has become a major technique for modelling hydrological time
series. Harms and Campell (
1967) proposed essentially the first disaggregation
approach. At that time, they termed their approach an extension of the Thomas

Flering
model (Thomas and Feiring, 1962) which was popular at that time. The Harms and
Campell model, while not having the m
athematical sophistication or completeness of
current disaggregation models, does posses most of the qualities desirable in
disaggregation models. It did provide a method for generating the proportions needed to
10
disaggregate an annual flow value. This mo
del comes surprisingly close to producing
the desired results but it has never caught on because of its very obvious theoretic
shortcomings. The concept itself is very robust with regard to the disaggregation model
choice.
The first well accepted disagg
regation model was presented by Valencia and
Schaake (1973). They introduced the basic disaggregation procedure which can be
preserve within

year seasonal (serial) correlation and the correlations between annual
and seasonal series. However, the procedur
e does not preserve the over the year
correlation coefficients of historic data. Then Mejia and Rousselle (1976) extended the
Valencia and Schaake (1973) approach intending to preserve the over

year seasonal
(serial) correlation (i.e. correlations of seas
onal quantities in two successive years).
They proposed a modification by adding a term to the Valencia and Schaake model to
overcome to overcome shortcoming of that models. This additional term contains as
many seasonal values in the previous years as d
esired. Unfortunately, it does not
perform as expected.
Mejia and Rousselle (1976) rated the Valencia and Schaake approach as “a
significant benchmark in the literature of hydrological time series”. The Mejia and
Rousselle model has an inconsistent str
ucture in which the problem of the parameter
estimation arises and thus, in theory, preserves non of the desired correlation (Lane,
1979; Stedinger and Vogel, 1984; Lin, 1990). Then several improvements are
introduced to the model to overcome this difficu
lty. Stedinger and Vogel (1984)
assumed that the random component of the model is itself autoregressive. Lane (1979)
and Lin (1990) introduced an additional moment equation procedure to make the set of
moment equations mathematically consistent. However
, the model still cannot
reproduce the over

year seasonal (serial) correlations for which it was constructed.
Several work have been proposed to reduce the difficulty of the large number of
the parameters appeared in the disaggregation models. Various c
ondensed
11
disaggregation models are suggested in the literature (e.g. Stedinger et al., 1985; Grygier
and Stedinger, 1988; Santos and Salas, 1992) to reduce the number of parameters.
However these models were not preserving explicitly many correlation coef
ficients of
the flow data. Lin and Lee (1992) developed a new parameter estimation method for the
Mejia and Rousselle disaggregation model. They provide the true linkage between the
aggregation and disaggregation approaches. In their study, it is recogn
ised that the
parameter estimation was based on the derived annual model and the fitted periodic
model.
Disaggregation is an approach which is an expedient way to generate very
reasonable data samples with all of the “important” statistics preserved wit
h number of
parameters with errors in the process “hidden” in inconsequential locations that is very
versatile. This approach was grown not from a theoretic background but from a
practical need. It uses, usually but not always, a simple annual model. Th
e
disaggregation model in effect only generates the proportions by which the already
generated annual data are distributed within the seasonal time segments. An important
concept that is not often stated in modelling is the concept of sweeping errors unde
r rug.
That is to spread errors to where they are neither noticeable nor important. This ties in
with the relevance of the eventual use of the generated data.
Hershenhorn and Woolhiser (1987) preserved a
parameter

efficient
model
for
disaggregating dai
ly rainfall into individual storms. The
model
allowed simulation of the
number of rainfall events (storms) in a day, and the amount, duration, and starting time
of each event, given only the total rainfall on that day and on the preceding and
following day
s. Twenty

three years of data for July and August, from a gage on the
Walnut Gulch Experimental Watershed, were used to find the appropriate
model
structure and to estimate parameters. Statistical tests indicated that simulated sequences
of storms compare
favorably with observed sequences, and that the
disaggregation
model
structure and parameters identified for one gage provide a satisfactory fit for three
stations.
12
Stochastically generated hydrologic data have used in the past by water
authorities world

wide for long term planning of water resources development projects.
These data are also currently being used in short term and medium term planning and
operation of water resource systems. For valid and realistic results, it is necessary that
the gener
ated data sequences preserve all statistical properties of historical data.
Maheepala and Perera (1994) presented an improved disaggregation method for
generation of alternative sequences of monthly hydrologic data. The method is designed
explicitly to p
reserve the over year monthly serial and cross correlations, in addition to
other monthly and annual parameters of the historic sequence. The method is applied to
both single site and multi site cases and compared with two other disaggregation models
that
are used in Australia. The comparison of results shows that the developed method
satisfactorily preserves both monthly and annual statistical parameters of the historic
data sequences including the over year monthly correlations.
Gyasi

Agyei (1999)
dem
onstrated how the Gyasi

Agyei
–
Willgoose hybrid
model for point processes could be regionalized for daily rainfall disaggregation using
limited high resolution data within a region of interest. Their model was a product of the
binary nonrandomized Bartlett
–
Lewis rectangular pulse model and a lognormal
autoregressive model used as a jitter. The computationally efficient multi normal
approximation to parameter uncertainty was used to group the monthly parameter values
of the binary model. For central Queens
land, Australia, it had been established that the
parameters of cell origins and the duration of the rectangular pulse of the binary model
could have constant values for all months. Second harmonic Fourier series was used to
represent the seasonal variati
on of the parameter governing the storm lifetime. The
storm arrival rate is a function of the daily dry probability and the other parameters.
Additive properties of random variables with finite variances were used to scale down
the daily mean and variance
of the historical data to the simulation timescale, values
required by the jitter model. The results of using observed daily rainfall statistics to
capture sub

daily statistics by the regionalized model were very encouraging. The
model is therefore a val
uable tool for disaggregating daily rainfall data.
13
A disaggregation methodology for the generation of hourly data that aggregate
up to given daily total is developed. This combines a rainfall simulation model based
upon the Bartlett

Lewis process with pr
oven techniques for the purpose of adjusting the
finer scale (hourly) values so as to obtain the required coarse scale (daily) values. The
methodology directly answers the question of the possible extension of the short hourly
time series with the use of
longer term daily data at the same point and provides the
theoretical basis for an operational use of this methodology when no hourly data are
avaible. The algorithm has been validated in full test mode in the case where hourly
data are avaible. Specific
ally, two case studies (from the UK and US) are examined
whose results indicate a good performance of the methodology in preserving the most
important statistical properties of the process (Koutsoyiannis and Onof, 2001)
Daily rainfalls are simulated thro
ugh a two station model at a key station and
satellite stations whilst maintaining the first three moments and relevant correlations.
Wet and dry runs of the occurrence process of daily rainfall are assumed to have a
geometric distribution. Disaggegration
of daily rainfalls into hourly values is made
through dimensionless accumulated hourly amounts generated by a beta distribution. It
is postulated that the occurrence process of hourly rainfall has also a geometric
distribution but it is conditioned on the
total daily rainfall. Application is made to the
Tevere (Tiber) basin in central Italy. The simple reduced parameter approach is seen to
reproduce satisfactorily extremes and other statistical properties of daily and hourly
rainfalls (Kottegoda et al.,
2002).
The basic goal of any disaggregation model is to allow the preservation of
statistical properties at more than level. Disaggregation modelling has two additional
attributes which make it attractive. First, it is a technique which allows for a re
duction
in the number of parameters with little or no corresponding loss of desirable properties
in the generated data. Second, disaggregation allows for increased flexibility in the
methods used for generation.
14
2.3.1.1
General Disaggregation Models
All disag
gregation models can be reduced to a form which may be termed the
linear dependence model. The linear dependence model is
Y = AQ + Bε
(2.1)
where
Y
is the current observation of the series being generated;
Y
is generated
dependent on the curren
t value of the
Q
series; ε represents the current value from a
completely random series (stochastic term); and
A
and
B
are the parameters.
In terms of the linear dependence model, the form would now become
Y = AQ + Bε + C
(2.2)
where
C
is param
eter matrix with the same dimension as
Y
. The values estimated for
A
and
B
would remain unchanged.
2.3.1.2
Single Site Disaggregation Models
Three forms of a single site temporal disaggregation are presented here: the basic
model; extended model; and the co
ndensed model. The basic model of Valencia and
Schaake (1973) disaggregation model form
Y
t
= AQ
t
+ Bε
t
(2.3)
The advantage of this model is its very basic clean form. The causal structure of
this model is designed to preserve variance and covariances among the seasonal values.
One disadvantage is that the moments being preserved are not co
nsistent. A second
disadvantage is that the number of the parameter is large.
15
The extended model, developed by Meija and Rousselle (1976), is an extension
of the basic temporal model. An additional term is included in the model to preserve the
seasonal
covariances between seasons of the current year and the seasons of the past
year.
It is still quite straightforward and clean. The problem of an inconsistent causal
structure is not corrected by the additional term and the problem of an excessive numbe
r
of parameters is made worse.
Lane (1979) has developed the condensed model. His approach essentially set to
zero several parameters of the Meija and Rousselle (1976) model which is not important.
This model is designed to preserve covariances betwee
n the annual value and its
seasonal values and to preserve variances and lag

one covariances among the seasonal
values. The main advantage of this model is the reduction of the number of parameters.
There are two major disadvantages. First, the model is
not as clean and straightforward
as the previous models. The second disadvantage is that since all seasonal are not
generated jointly, the seasonal data will not add exactly to give the annual time series.
This problem can be dealt with in two ways. On
e is to assume the seasonal data are
satisfactory and to recalculate the annual time series. The second and generally more
preferable approach is to adjust the seasonal flows so that they add up exactly to the
annual values. The benefit of the parameter
reduction far outweighs these shortcomings.
2.3.1.3
Multi Site Disaggregation Models
Simply stated, the only difference between the multi site disaggregation and the
single site methods just discussed is that the matrices are larger. The multi site case doe
s
not require any new model forms, but only some minor complications because the
moment matrices are much larger. The biggest effect is that the number of parameters
16
and moments involved increase at a rate roughly proportional to the square of the
number
of sites.
Since the effect of going from single site to multi site applications is basically the
same for all approaches, only the extended model will be examined. The model still has
the form
Y
t
= AQ
t
+ Bε
t +
CY
t

1
(2.4)
where
Q
is not only a
single value, but is a column vector which contains an annual
value for each site. Likewise, the numbers of generated values in
Y
have increased so
that
Y
now contains a complete set of seasonal data for each site. The numbers of
stochastic terms contain
e
d in matrix ε are also increased. If there are n seasonal and z
seasons included in matrix
Y
t

1
.
The advantage of multi site approach over multiple applications of a single site
approach is the preservation of some additional correlations. These are c
ross

correlations between the values at the various sites. The disadvantage is that in order to
preserve these additional correlations, additional parameters are also required.
2.3.1.4
Spatial Disaggregation Models
The form of spatial disaggregation model u
sed by Lane (1979) is
Y
t
= AQ
t
+ Bε
t +
CY
t

1
(2.5)
where Y
t
is a column matrix of the current substation annual values being generated,
Q
t
is a column matrix of current key station annual values (note that the model is not
restricted to only one station),
Y
t

1
is a column matri
x of the previous matrix of the
previous substation annual values.
A, B
and
C
are parameter matrices
.
17
This model is very similar in form to the Meija and Rousselle temporal
disaggregation model upon which it is based. With all disaggregation approaches,
the
spatial disaggregation can be staged.
2.3.1.5
Parameter Estimation for Disaggregation Models
The parameters of disaggregation models have traditionally been estimated using
the method of moments. This technique is rather straightforward in its applicati
on. It
avoids trial and error, iterative procedures and implicit solutions which found in some
other parameter estimation approaches.
The method of moments estimates will be presented only for the basic
disaggregation model. The estimates are presented
without derivation. For other model
parameter estimates and for the derivations of the estimates, the reader is urged to refer
to Valencia and Schaake (1973), Mejia and Rousselle (1976), Salas et al. (1980), Lane
and Frevert (1988), Grygier and Stedinger
(1985) and Loucks et al. (1981).
2.4
Aggregation Model
The aggregation methods generate the seasonal series and the annual series are
derived from the aggregated synthetic seasonal series. The periodic ARMA and SVD
combined models can be classified as
the aggregation methods. The periodic AR can be
expressed as PAR and the periodic ARMA can be written as PARMA. The PAR (1) is
commonly known as the Thomas

Fiering model. This model has been widely used for
data generation and forecasting of hydrologic
variable in general and streamflow series
in particular. Since then, there is an increasing use of the PARMA (1, 1) model for the
modelling seasonal hydrologic variable (Delleur et al., 1976; Salas et al., 1980, 1982;
Obeysekera and Salas, 1986; Lin and L
ee, 1992). Thomas and Fiering’s (1962) early
18
model and its periodic autoregressive moving average (PARMA) extensions generate
monthly or seasonal flow directly which can be summed to obtain annual.
Delleur et al. (1976) studied the periodic ARMA models
for generating of flows
for the Salamonie River at Dora, Indiana. There are 12 seasonal correlation coefficients
in the case of monthly series. In their work, the seasonality of the AR and MA
coefficients are expressed in the Yule

Walker equation. Delle
ur et al. (1976) explained
about the correlation coefficients are affected by the condition of the season. Wet
seasons are associated with rapid direct runoff fluctuations resulting low values of the
seasonal correlation coefficient. Similarly, dry seaso
ns associated with the groundwater
depletion and yield a high correlation coefficient. The monthly flow of Salamonie River
exhibits a strong serial dependence when model with standardised logarithms of monthly
flows. Delleur et al. (1976) described that
the seasonal effect appear to be stronger on
the MA coefficient than on AR coefficient. The AR coefficient is related to the storage
of the watershed, which varies more slowly with time than does the MA coefficient,
which is related to rainfall input. Hi
gher

order model of periodic ARMA (Delluer et al.,
1976) will yield coefficients exhibiting larger seasonal affects, since their estimates
depend on larger lags of the seasonal effects.
Salas et al. (1980) explained in detailed in detail the application
of the periodic
AR and ARMA models in the book “Applied Modelling of Hydrologic Time Series”.
The book is considered the best book as reference in the work related to the application
of PARMA models. Salas et al. (1980) explained the fundamental of perio
dic ARMA
models and deriving the equations precisely. The work by Salas et al.(1982) related to
the application of Yule

Walker equation for ARMA (p,q) models with periodic
parameter. Derivation of the ARMA (p,q) equations is illustrated. They used momen
t
estimates to solve the systems of equations. The estimation of parameters is illustrated
by Salas et al.. (1982) for the periodic models of order ARMA (0,1), ARMA (1,1) and
ARMA (2,1). Further these works were continued by Obeysekera and Salas (1986) i
n
the application for the seasonal streamflow series. The study restricted to application of
PAR (1) and PARMA (1,1) models for the seasonal series. Derivation is made for the
19
models and properties of the corresponding annual series. Seasonal and annual
flows of
the Niger River are used to illustrate some of the estimation procedures, Lin and Lee
(1992) used the 47 years of streamflows of the Tanshui River at Guishan to demonstrate
the application of the PAR (1) and PARMA (1,1) models. They found that
the
modelling based on the PARMA (1, 1) model can reproduce more historical moments
than that based on the PAR 91) model. Between the two periodic models considered in
the applications, the PARMA (1, 1) model is to be preferred.
The periodic autoregres
sive moving average model may not capture the
distribution and persistence of annual totals (Grygier and Stidinger, 1988). Recently
Chavalit and Nguyen (1994) proposed the approach of generating synthetic monthly net
basin supply of Great Lakes water reso
urces system, Canada. The proposed procedure
consists of the combination of a singular value decomposition (SVD) technique matrices
(see, e.g. Joreskog et al., 1976) and first order univariate AR(1) or multivariate
autoregressive process MAR(1). The adva
ntage of this procedure is that parameter
estimation is simple. The SVD

MAR (1) procedure was shown assured the preservation
of means, standard deviation and within the year correlation matrices at all successive
aggregation levels. The SVD combine model
proposed by Nyugen and Chavalit (1994)
is relatively simple compared to the other generation models. Besides with the
advantage of simple in calculation procedure but the SVD combine models possess its
weakness tested with transformed net inflows data se
ries.
Models with periodic parameters are referred to herein as models (Salas et al.,
1980; Vecchia et al., 1983). There are two seasonal periodic models will be applied in
the simulation study such as net inflow. Those are the periodic autoregressive
PAR (1)
and periodic autoregressive moving average PARMA (p, q) models. The method of
seasonal periodic models was explained in detail by Salas et al. (1980, 1996). The PAR
(1) models has been widely used for data generation and forecasting of hydrologi
c
variables in general and streamflow in particular. This model commonly known as the
Thomas

Fiering model. Recently there were in increasing use of PARMA (p, q) models
20
for modelling seasonal hydrologic variables (Obeysekera and Salas, 1986; Lin and Lee,
1992, 1994; Salas et al., 1996).
Chavalit and Nguyen (1994) proposed the procedure consists of the combination
of a singular value decomposition (SVD) technique of matrices and first order univariate
AR (1) or multivariate autoregressive MAR (1) proce
ss. The proposed SVD combine
models are divided into two section; first are the AR(1)/SVD and MAR(1)/SVD models
and second are the SVD/AR(1) and SVD/MAR(1) models (Sobri, 1999).
2.5
Evaluation the Performance of Simulation Models
Comparing the stati
stical properties (statistics) of the process being modelled is
the evaluation the properties of the process. Generally, one would like the model to be
capable of reproducing the necessary statistics that affect the variability of the data. The
model als
o should be capable of reproducing certain statistics that are related to the
intended use of the model. Further, the reliable models are chosen and will be simulated
for the properties of model. Generally, the statistic properties that is important thes
e
studies are the seasonal mean, standard deviation, variance, skewness and correlation.
2.6
Stochastic Analysis, Modelling and Simulation (SAMS 2000)
Several computer packages have been developed since 1970’s for analyzing the
stochastic characteris
tics of the time series in general and hydrologic and water
resources time series in particular. For instance, the LAST package was developed in
1977

1979 by US Bureau of Reclamation (USBR) in Denver, Colorado. Originally the
package was designed to run
on a mainframe computer but later it was modified for use
on personal computers. While various additions and modification have been made to
LAST over the past twenty years, the package has not kept pace with either advances in
21
time series modelling or adv
ances in computer technology. These facts prompted USBR
to promote the initial development of SAMS, a computer software package that deals
with the seasonal streamflow series. It is written in C and Fortran and runs under
modern windows operating systems
such as WINDOWS NT and WINDOWS 98. This
first version of SAMS (SAMS 96.1) was released in 1996. Since then, corrections and
modifications were made based on feedback received from the users. In addition, new
functions and capabilities have been limitat
ions.
SAMS has been developed as a cooperative effort between USBR and Colorado
State University (CSU) under USBR Advanced Hydrologic Techniques Research
Project trough an Interagency Personal Agreement with Professor Jose D.Salas as
Principal Investigat
or. Drs. W.L.Lane and D.KFrevert provided additional expert
guidance and supervision on behalf of USBR. Several former CSU graduate students
collaborated in various parts of this project including, M.W.Abdel Mohsen, who
developed many of the Fortran code
s, M.Ghosh who initiated the programming in C
language followed by Mr. Brans;ey Jones, Nidhal; M.Saada and Chen

Hua Chung.
SAMS is a computer software package that deals with the stochastic analysis,
modelling and simulation of hydrologic time series.
The package consists of many
menu option windows which enables the user to choose between different options that
are currently available. SAMS 2000 is modified and expanded version of SAMS 96.1.
It consists of three primary application modules:
a.
Statist
ical Analysis of Data
b.
Fitting a Stochastic Model (includes parameter estimation and testing)
c.
Generating Synthetic Series
22
2.7
Summary of Literature Review
The study of time series analysis is required in the reservoir simulation studies.
Previou
s illustrated search through the literature of time series analysis reveals the
disaggregation and periodic models are both the well known approach of synthetic data
generation in hydrology and water resources. The disaggregation approach means that
in or
der to generate say monthly flows or rainfalls, the annual flows and rainfalls are
generated first, then they are disaggregated into monthly values by some appropriate
scheme. In this study, disaggregation approach is the model that use and focus to
gener
ate rainfalls for rainfall

runoff application. Disaggregation modelling has major
advantages over other modelling techniques. It is easily understood, easily applied and
very flexible. There are opportunities to use long term memory models and to includ
e
parameter uncertainty. SAMS is used to simulate the rainfalls data with disaggregation
method such as Valencia and Schaake, Mejia and Rousselle and Lane. SAMS is a
software package for analyzing the stochastic characteristics of time series in general
and hydrologic and water resources time series in particular.
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