| This study of the
behaviour of rainfall dynamics at different temporal scales identifies the type
of approach most suitable for transformation of rainfall
data from one scale to another. Rainfall data of four different temporal scales,
i.e. daily, 2-day, 4-day and 8-day, observed over a period
of about 25 years at the Leaf River basin, Mississippi, USA, are analysed. The
correlation dimension method is employed to identify the
behaviour of rainfall dynamics. The finite correlation dimensions obtained for
the four rainfall series (4.82, 5.26, 6.42 and 8.87, respectively) indicate
the possible existence of chaotic behaviour in the rainfall observed at the four
scales. A possible implication of this might be that the rainfall
processes at these scales are related through a chaotic (scale-invariant)
behaviour. However, a comparison of the correlation dimension and
coefficient of variation of each of the time series reveals an inverse
relationship between the two (higher dimension for lower coefficient of
variation and vice versa). The presence of a large number of zeros in the higher
resolution time series (that could result in an underestimation of
the dimension) and the possible presence of a higher level of noise in the lower
resolution time series (that could result in an overestimation of
the dimension) might account for such results. In view of these problems, it is
concluded that the results must be verified using other chaos identification
methods and the existence of chaos must be substantiated with additional
evidence.
Keywords: rainfall, chaos, scaling, correlation dimension, number of variables,
coefficient of variation, data size, noise, zeros |