Time Series Modeling - Water Quality Management: Assessment and Interpretation - page 40

effect relationship, and the
models could occasionally be built by knowing the structural relations between
components of a system. These relations are usually expressed in terms of differ-
ential equations whose solutions provide the desired models. Considering the
independent variable is time, the resulting model can explain the variation of a
system component or the whole system with respect to time. This makes it possible
to forecast the future values of time dependent trends and other characteristics quite
accurately. However, due to the presence of various unknown factors in nature,
models are not completely deterministic. Therefore, in most cases it is required to
study various phenomena under uncertain conditions, resulting from the effects of
unknown factors. This leads to consideration of stochastic modeling.
In this approach, one is only able to make probabilistic statements about the
relation between system components and their future values. A good example of
this approach is stochastic hydrology. Numerous studies have proved the suitability
of statistical methods in various hydrological problems. Especially, when the var-
iation of the magnitude of one or more parameters of water quality is studied as a
function of time, statistical method known as time series analysis are very helpful.
By these methods, one can identify the trends, the periodic changes, and the random
parts present in the natural series of data. Identi

The deterministic approach is based on a cause

-

cation, estimation, and subsequent
synthesis of these model components envisage the future path of the series, which
in turn could help to take control measures (Bowerman and O ' Connell 1987 ).

4.2 Historical Background

The emergence of stochastic hydrology goes back to 1914 when estimated the
“ . The arrival of digital computers provided suitable means

for application of complex methods for statistical analysis such as time series.
Early applications of time series approach analyzing water resources were
undertaken by Thomann ( 1967 ) who studied the time variation of temperature and
dissolved oxygen of the Delaware Estuary. The data were obtained by continuously
recording monitoring stations, operated jointly by the US Geological Survey
Department and the city of Philadelphia. Carlson et al. ( 1970 ) and McMichael and
Hunter ( 1972 ) have reported the successful use of Box-Jenkins method for time
series analysis. The former applied this method to model and forecast annual stream

probability of dry year ”

cant reductions in variance with one or two parameters is
reported to be achieved. Other researchers use this method in developing models for
daily temperature and

flow data, where signi

flow in rivers. These models also incorporated deterministic
components, which was preferable from a numerical and a rational point of view to
a purely stochastic or purely deterministic model.
The Box-Jenkins method of time series analysis was applied in modelling the
hourly water quality data recorded in the St. Clair River near Corunna, Ontario for
chloride and dissolved oxygen level by Huck and Farquhar ( 1974 ). The models
were parsimonious and physically reasonable and successful results were obtained.