Richard Eyckholt

Department. of Physics

Colorado State University

Rainfall data shows evidence of low-dimensional chaos, but streamflow
data does not, which is surprising for streamflows that come from
rainfall. However, there are problems with the analysis of streamflow
data. One problem is that the data sets are so small that finding
the correlation dimension is not an easy matter, and even finding an appropriate
delay time

can be problematic. Thus, we developed the C-C method for dealing
with such small data sets. This method does a good job of finding
an appropriate delay time, as well as an appropriate delay time window.
I will discuss this

method and show that the use of the delay time window, rather than
the delay time, makes it easier to find the correlation dimension
for small data sets. While this method leads to improved analyses
of rainfall data, streamflow data still fail to how evidence
of low-dimensional chaos. The problem may lie in the aggregation
and sampling processes involved in streamflow data. I will show how
such aggregation and sampling can obscure the nonlinear determinism in
a low-dimensional chaotic system.