That hydrologic phenomena are stochastic is a conventional wisdom (Tanimoto 1993) that facilitates substitution of mathematical analysis for data. However, H. E. Hurst (1951,1965) in his studies to determine the yield of Aswan High Dam analyzed 120 records ranging from 10 to 2,000 years, and found that the duration of wet or dry periods was longer than for random events that the means varies over time i.e., the means for major segments of very long time series are different than the mean for an entire period. These characteristics of natural time series have been designated " Hurst Phenomena" (Bras and Rodriguez-Iturbe, 1985) . Hurst's relationship between length of record (N), standard deviations (S), and range of accumulated deviation of the means is useful for evaluating and interpreting hydrologic time series.

The relationship is R/S = (N/2)k. The exponent, k, is a measure of persistence of wet or dry periods. Hurst found the average value of k for hydrologic data to be 0.72, whereas the value for random data is 0.50. The effect of assuming stochasticity for hydrologic phenomena is to greatly underestimate R. Also, a much larger S would be required to explain the actual data.

There appear to be differences in the patterns of generally wet, normal, or dry periods. In Figure 1, bars have been drawn to represent the duration and magnitude of the means of generally wet and generally dry periods. The bars indicating wet periods extend from lowest valley to highest peak of a series of accumulated deviations from the mean, and the bars indicating dry periods extend from highest peak to lowest valley. The few occurrences of near-normal periods are similarly indicated. The Colorado River pattern is a mixture of very long and quite short periods.

Wet and dry periods that persist longer than probable for random events, and the existence of regional patterns should be considered in the species selection, and timing of planting aspects of revegetation and range improvement, afforestation and riparian restoration. Sustainability will depend in large part on the ability of selected plant materials to exist and flourish throughout the range of climatic variation.

Hurst, H.E., 1951. Long-term storage capacity of reservoirs. Trans. ASCE, 116: 770-779

Hurst, H.E. R.P. Black, and Y.M. Simaika. 1965 Long-term storage. Constable, London, U.K. 145 pp.

Tanimoto, P., 1993. Considerations of stochasticity in ecosystem management. Watershed Management Council Newsletter, 5:2:13. Spring 1993

Turner, K.M. 1992. Reliability of storage schemes, tree rings, and Hurst phenomena; in; Proceedings of the American Geophysical Union Twelfth Annual Hydrology Days, Colorado State University, Fort Collins, Colorado, April 1992. Hydrology Days Publications, Atherton, California. pp 230-242.