Geology Reference
In-Depth Information
Information theory is a widely used mathematical theory in electronics and
communication. Information theory has two primary goals: (i) to develop the fun-
damental theoretical limits on the achievable performance when communicating a
given information source over a given communications channel using coding
schemes from within a prescribed class; (ii) to develop coding schemes that provide
performance that is reasonably good in comparison with the optimal performance
given by the theory. More detailed concept of Information Theory and Entropy can be
found in Gray [
38
]. The capability mentioned in the
first goal could be used for data
quality assessment. In information theory, entropy is often referred as Shannon
entropy which measures the uncertainty and randomness associated with a random
variable. Capabilities of Shannon entropy to measure the average information content
associated with input data series are explored in this topic. Despite the claimed
success of the methods from the aforementioned literature, there is a lack of com-
parison with conventional methods, data splitting approaches like cross validation
approaches and cross correlation approaches. This topic aims at comparison and
assessment of model input selection based on the Gamma Test, entropy theory, AIC
BIC and the above mentioned traditional benchmarking approaches in modelling.
This topic makes an effort to comment on another rising debate in data based
modelling in hydrology: should the input data be treated as signals with different
frequency bands so that they could be modelled separately? Wavelet theory is a
novel field of mathematics, which recently gained attention among scientists
studying acoustics,
fluid mechanics, and chemistry. The concept of wavelet trans-
formation involves representation of a general signal or time series in terms of
simpler,
fixed building blocks of constant shape but at different scales and positions.
Discrete Wavelet Transforms (DWT) can give very useful decomposition of time
series in such a way that faint inherent temporal structure of the time series can be
revealed and can be effectively handled by the above mentioned and used non-
parametric models in this topic. This capability has been used effectively in various
fields of engineering for dealing issues in noise removal, object detection, image
compression and structural analysis [
89
]. Unlike Fourier transforms, wavelets have
an ability to elucidate simultaneously both spectral and temporal information within
the signal whereas Fourier spectrum contains only globally averaged information.
This property overcomes the basic shortcoming of Fourier analysis in modelling.
Therefore, data pre-processing can be carried out by time series decomposition into
its subcomponents using wavelet transform analysis [
73
]. The wavelets can express
original signals as additive combination of wavelet coef
cients at different reso-
lution level. A study by Aussem et al. [
13
] was the
first hybrid ANN-wavelet
conjunction model in which they used it for
financial time series forecasting. Later
Zhang and Dong [
104
] proposed a short-term load forecast model based on multi-
resolution wavelet decomposition with ANN model. The
first application in
hydrology was in 2003 when Wang and Ding [
100
] applied wavelet-network model
to forecast shallow groundwater level and daily discharge. In the same year Kim
and Valdes [
52
] applied this conjunction model concept in coupling dyadic wavelet
transforms and ANNs to forecast droughts for the Conches river basin. Keeping the
success stories of the aforementioned literature in mind, this topic attempts to
