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36 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS In its present (1965) state of development, multivariate lLIlalysis is- not a useful tool for defining cause-and-effect relationships in hy- drology; regression analysis is still the best method available. Characteristics of Hydrologic Data / Streamflow is a continuous process which varies with time, and thus streamflow data are said to form a time series. A plot of streamflow against time would show a pattern of variation recurring each year; that is, high flows tend to occur at particular times of the year and low flows at others in response to climatological characteristics which also vary seasonally. Because streamflows are not discrete values, we need to chop the hydrograph into pieces which we will consider as individual stream- flows. The p'!J"ticular pieces we use have certain characteristics which must be considered in analysis. The most common piece is the daily mean discharge. A daily mean discharge is related to the discharge of the previous day and lies within a range which depends on the time of year. In statistical terms, daily mean discharge is a serially correlated variable, that is, it is nonrandom. The daily mean discharges for a year are also not homogeneous; they are more likely to be larger at one time of the year than at another. Data are considered homo- geneous if any subgroup to which certain of these data may be logically assigned has the same expected mean and variance as any other subgroup of the population. Monthly mean discharges for different calen- dar mon ths are also serially correia ted and nonhomogeneous. Annual mean discharges may be homogeneous values. They mayor may not be serially correlated, depending on the amount of basin storage at the time that the hydrologic year begins. Instead of a streamflow variable made up of adjacent segments of a hydrograph, we may consider variables such as July mean, annual peak discharge, or annual minimum flow. These variables are made up of one individual from each year and thus are independent of the yearly cycle of streamflow. They are also inde- pendent of each other (with the possible ex- ception of annual minimum flows which include eflluent from ground-water recharge of a previous year). Precipitation, temperature, sediment dis- charge, water quality, transpiration, evapora- tion, lLIld solar radiation vary throughout the year; indices describing them may be nonran- dom and nonhomogeneous. Obviously the distinction between random and nonrandom data and between homogeneous and nonhomogeneous data is not always clear cut. The analyst will have to determine whether the effects of possible moderate nonrandomness or nonhomogeneity will invalidate the conclu- sions of his particular analysis. It is im portan t that the character of the data be considered in designing the analysis and in interpreting the results. So- far we have described variables that may be considered samples from a population if the individuals are homogeneous. If the individuals are also random, we can estimate the frequeucy distribution of the variable from the sample. Another type of variable used extensively in hydrology cannot be considered to have a probability distribution, or even to be drawn from a population as thought of in the usual sense. Basin characteristics such as drainage area, slope, elevation, and vegetal index are in this category. (It is possible to concrive of certain physiographic parameters as random variables, but rarely can the available sample be considered randomly selected or represent- ative.) Time is sometimes used as a variable in regression. It has uo distribution and is used only as a substitute for the real factor or factors (which are unknown or cannot be ex- pressed by indices) associated with changes in a dependent variable. . . Effects of data characteristics on analysis We prepare a frequency distribution of daily mean discharges from several years of data; this. is the duration curve. The individual values are nonrandom and nonhomogeueous. Therefore the duration curve cannot be con- sidered a frequency curve. The probability of exceeding a certain value on a particular future day depends both on the preceding value and .