Several statistical tests are performed on streamflow series for purposes of analyzing multiyear drought events. These statistical tests on both high-flow and drought event parameters include (1) stationarity in terms of their linear trend; (2) randomness in terms of lag-1 serial correlation; (3) correlation and cross correlation between these parameters (duration, magnitude and severity). The test results and their implications are discussed in relation with the characterization of high-flow and drought event series. Two types of envelopes for drought duration and severity are presented which use Tschebycheff's inequality. These envelopes give an excellent indication of the maximum response of a watershed in terms of drought duration and severity during the period of record.
INTRODUCTION
Knowledge concerning hydrologic drought (extended periods of below normal streamflow) is an important aspect in the planning of water resource systems and in the allocation of available stream flows among a variety of competing uses.However, the study of droughts in terms of duration, magnitude (average deficit), and severity (total deficit) is one of the most seriously neglected aspects of the science of hydrology. Relatively, little attention has been given to the quantitative and qualitative aspects of drought analysis. Much of the existing drought studies refer to specific basins or particular historical droughts. Notable exceptions, however, include Huff and Changnon [1964], who developed a method of estimating drought streamflow frequency by using low precipitation frequency and a single geomorphic index; Whipple [1966], who applied the station-year method of regional frequency analysis to multiyear hydrologic droughts; Yevjevich [1967], who applied the statistical theory of runs to the analysis of drought events; and Askew et al. [1971], who observed that existing synthetic streamflow generation models fail to accurately reproduce historical critical periods.A thorough understanding of drought parameters is required for the development of a stochastic model that will generate drought events and would be useful in devising valid methods of performing regional drought frequency analysis.
METHODOLOGYBefore proceeding, it is necessary to define the type of hydrologic event being dealt with in this paper. In a previous paper [Dracup et al., 1980], we outlined four decisions to be made in arriving at a viable drought definition: the nature of the water deficit (e.g., precipitation, soil moisture, streamflow), the basic time unit of the data (e.g., month, season, year), the truncation level, which distinguishes low flows from high flows (e.g., mean, median, mode), and the regionalization and/or standardization approach. This paper is concerned with streamflow drought only. Although periods of low precipitation clearly have a dominant impact on periods of low runoff, only the characteristics of these low runoff periods are considered. Considered here are extended low-flow periods lasting 1 year or more, and hence annual streamflo...
