Modeling

Generation of Long-term Rain Input 93
There is, however, currently no model that can directly disaggregate daily
rainfall into 1-15 minute rainfall. Also, available disaggregation models cannot
extend the length of the rainfall data, they only artificially enhance the time
resolution of the data.
Most stochastic models attempt to model occurrence and duration of both
wet and dry events (intermittency) coupled with another algorithm to determine
precipitation amounts for the wet events. These increasingly complex models do
not, however, provide any explanations relating to processes that drive the
rainfall phenomenon (Yevjevich, 1991). Rainfall is a complex atmospheric
process that is affected by incident solar radiation, sunspot activity, lunar orbits,
the El Niño-Southern Oscillation (ENSO) phenomenon, wind circulation
patterns, etc. Models based on probabilistic outcomes and parameter fitting
without any correlation to physical processes are insufficient and dishonest
(Klemeš, 1986).
Within the stochastic modeling approach, there is interest in developing a
general theory to characterize the internal structure of rainfall. By examining the
internal structure of rainfall, hydrologists attempt to describe the link between
the observed rainfall and the mechanisms responsible for its occurrence.
Estimating the properties of the underlying processes that lead to an observed
series is termed TS analysis (Bras and Rodriguez-Iturbe, 1985). TS analysis
models of rainfall attempt to analyze trends, periodicities, and frequencies in
order to describe, explain, and simulate rainfall rates. TS analysis is also being
used to correlate climate patterns such as between rainfall and other physical
phenomena.
Wavelet analysis is a new tool that can be used for time-analysis of multifrequency,
multi-scale signals that may be non-stationary or non-sinusoidal in
structure (Bradshaw & McIntosh, 1994). Wavelets and wavelet transforms offer
many advantages over traditional Fourier transforms, which are inadequate for
analyzing non-stationary, variable, and intermittent data such as rainfall.
6.2 Review of rainfall modeling and analysis techniques
There are many rainfall model and analysis tools, each utilizing different
temporal and spatial scales (Berndtsson and Niemczynowicz, 1988). For the
sake of brevity, only a few model types from each approach are briefly
mentioned here.
The common origins of all rainfall models can be traced back to the late 19 th
century where engineers required design flows for hydraulic structures such as
sewers, open channels, and reservoir systems (Todini, 1988). The main focus
for urban hydrologists has been to determine the return period, or return
frequency, of extreme hydrologic events (Niemczynowicz, 1994). I-D-F curves
were developed as a packaged representation of recorded rainfall data for a
geographic region. These I-D-F curves provided average rainfall intensities as a