  A number of different analysis techniques have been used to analyze long-term
time series data from different rivers, starting with the determination of the
Hurst coefficient. We summarize the concept of fractals, multifractals and
Fractional Brownian Motion (FBM), and apply some such techniques to daily
stream flow data from the Parana River recorded at Corrientes, Argentina, for
106 years. After determining the Hurst coefficient for the entire data set (H =
0.76), we analyze the data for each of four seasons and draw the corresponding
FBM graphs and their multifractal spectra (MFS). Three of the seasons are
similar, but autumn is very different for both FBM and MFS. Based on the MFS
results, we propose a number of indices for measuring variations in stream
flow, and determine the values of the indices for the three similar seasons.
The indices are based on important parameters of the multifractal spectra. The
geometry of the spectra as well as the indices all indicate that Winter is the
most stable season. This is in contrast to the Boxplot of seasonal stream flow
data where Winter shows the largest variation. Thus, these indices provide
insight into river flow stability, not detected in, and indeed contradictory
to, that from basic statistical analysis.
