Geology Reference
In-Depth Information
Evapotranspiration is considered as an incidental, nonlinear, complex, and
unsteady process so it is dif
cult to derive an accurate formula to represent all the
physical processes involved. For this reason a new trend of use of nonlinear data
mining techniques such as fuzzy logic, ANNs ANFIS, SVMs, polynomial function,
Local Linear Regression (LLR), Bayesian networks and decision trees, etc. was
introduced. A paper by Keskin et al. [
45
] examines the potential of the fuzzy logic
approach in estimation of daily pan evaporation. Some typical studies reported so
far are ANNs in modeling daily soil evaporation [
30
], daily evapotranspiration [
52
],
daily pan evaporation [
46
,
48
,
84
,
87
,
88
], and hourly pan evaporation [
85
]. Using
temperature data alone, Sudheer et al. [
84
] found that a properly trained ANN
model could reasonably estimate the evaporation values for their study area in a
temperate region. From those reports, it is clear that ANN models are superior to the
conventional regression models, since ANNs do not require any predetermination
of regression forms. This advantage becomes more promising when an engineering
problem is too complex to be represented by regression equations [
56
,
85
] present a
review of 43 papers dealing with the use of ANNs on the prediction and forecasting
of water resources variables. The objective of this chapter is to provide mathe-
matical consideration and architecture of different AI and data-based models used in
this topic. Later in this chapter we describe a novel approach of hybrid modeling in
coupling wavelet transform with basic AI techniques.
4.1 Transfer Function Models
Time series analysis-based Transfer Function (TF) models are powerful tools to
determine dynamic and ef
uencing
variables in a real system. Many researchers have shown that TF based time series
models provide an empirical method for stochastic simulation, predicting, and
forecasting the behavior of uncertain hydrological systems with reasonable accu-
racy in the forecast [
92
]. TF models are often preferred to mathematical models and
physical models in hydrology, in situations such as those with limited data (no data
except the hydrological time series) or if available variable response is limited and
does not appropriately represent hydrological processes. Though many nonlinear
TF models have been developed recently, the modeling capabilities of linear time
series models remains unaltered. This subsection describes two famous and widely
used TF models, namely AR models, MA models, ARMA models, ARX, and
ARMAX. These two models were used in this topic for rainfall-runoff modeling
case study. Box and Jenkins [
13
]
cient models in order to de
ne and control in
first introduced ARIMA models based on key
concept of stationarity of the time series. ARIMA means Autoregressive Integrated
Moving Average models. The time series possesses stationarity if it (1) exhibits
mean reversion in that it
nite
variance that is time-invariant, and (3) has a theoretical correlogram that diminishes
as the lag length increases.
fluctuates around a constant long-run mean, (2) has a
