Chaos in rainfall: variability, temporal scale and zeros

A recent study on rainfall observed at the Leaf River basin reports that the presence of a large number of zeros in the data significantly underestimates the correlation dimension. The present study attempts to verify such a claim, by making predictions and comparing the results with the correlation dimensions. A nonlinear prediction method, which uses the concept of reconstruction of a single-variable series in a multi-dimensional phase space to represent the underlying dynamics, is employed. Correlation dimension analysis of only the non-zero rainfall series is also carried out for further verification. Rainfall data of four different temporal resolutions (or scales), i.e. daily, 2-day, 4-day and 8-day, are analyzed. The predictions for the finer-resolution (i.e. higher-resolution) rainfall are found to be better than those obtained for the coarser-resolution (i.e. lower-resolution) rainfall and seem to be consistent with the variability vs. predictability logic in a deterministic sense, i.e. higher prediction accuracy for data with lower correlation dimension and vice versa. An important implication of this result is that the presence of (a large number of) zeros in the rainfall data may not always result in an underestimation of the correlation dimension. The correlation dimensions estimated for the non-zero rainfall series are not significantly different when compared to those obtained for series including zero values, supporting the above. These results suggest that the low correlation dimensions for rainfall (in particular finer-resolution ones that commonly have a large number of zeros), as reported by past studies, could well be, or at least closer to, the actual dimensions of the rainfall processes studied.