Vujica Yevjevich

Transfer of hydrologic information among river points

Abstract Concepts of transferable and transferred information are used in transferring hydrologic information between the river points. The former is measured by the square of entropy coefficient and the latter by the square of correlation coefficient. The entropy coefficient measures the maximum transferable information. The transfer of information along rivers has two cases. One case is when the flows of upstream stations pass through downstream stations. These upstream flows are conceived as throughflow, which along with the intermediate flow constitutes the downstream flow. The other case is when the correlation is carried out between upstream flow and the intermediate flow of downstream stations only. Daily flows of three gauging stations of the Esencay River, Turkey, are used for demonstration purpose. Series are further structurally decomposed (original data, trends removed, periodicity removed, stochastic dependence removed), in order to see effects of these characteristics on the transferable and transferred information. Some basic similarities in deterministic components of river flows are the main contributors to transferable and transferred information. The study of lag cross-correlation showed a significant increase in transferred information.

Extremes in Hydrology

Several variables are needed for proper description of extremes in hydrology, such as peaks or lowest values, volume of excess or deficit, time duration above or below a critical value, etc. Selections of the type of extremes and the underlying hydrologic processes are needed in definition of extremes.

Experimental verification of the Dressier curved-flow equations

The Dressier equations with flow resistance and varying channel width for unsteady free-surface flow over curved beds are presented, and a generalized Bresse profile equation for steady curved-flow is derived. Experimental measurements on steady flow over a highly curved spillway demonstrate that the Dressier equations predict the free surface, the bed pressure, and the tangential flow velocity distribution accurately, but the predictions by the classical Saint-Venant equations are almost meaningless. Since both theories require gradual variations in bed geometry, applications to intervals with rapid changes are not valid. For the small intervals of our spillway geometry where the curvature and its derivative vary rapidly, the Dressier solution shows small, but rapid, variations, whereas the measurements indicate a more gradual variation over wider intervals.

HYDRAULIC-RESISTANCE TERMS MODIFIED FOR THE DRESSLER CURVED-FLOW EQUATIONS

The well-known empirical hydraulic-resistance terms, in common use with the Saint-Venant equations, are here modified to the specific functional form necessary for their use with the Dressier equations for curved open-channel two-dimensional flow in rectangular channels. From the general resistance term three cases are considered for three regimes of turbulent flow: the Blasius “smooth” flow; the Chezy “transitional” flow; and the Manning “rough” flow. These new functions are compared with the analogous terms in common use with the Saint-Venant equations. The modifications needed for the Dressier equations for the Chezy and Manning regimes are incorporated in two extra factors, am and av. The am factor is a given function of channel bottom curvature κ and of flow perpendicular thickness N, expressing the mass change affected by a boundary drag when flow is over a convex or concave bottom. The av factor is a given function of κ, N, and channel width w, expressing the modification required in bottom velocit...

Basic structure of daily precipitation series

Abstract Daily precipitation series exhibit intermittency, periodicity and stochasticity. To show it, three stations are used as examples. All series parameters, even descriptors of intermittency (probability of zero precipitation, run-lengths of zero and non-zero values), are highly periodic. Periodicity curves are estimated by averaging 365 daily values over intervals of 14, 28 or 61 days. Coefficients of variation, skewness and kurtosis, because of their definitions, show less periodicity than other parameters.

Research Needs on Flood Characteristics

Flood risk is nature related. Flood uncertainty is investigation related. The former can be changed only by changing the characteristics of floods. The latter can be changed only by more observation and investigation. The question to be answered yet is whether or not there is a physical upper bound to flood magnitude. The concept of probable maximum precipitation (PMP) seems to imply that there is an upper bound to flood magnitude. Flood characteristics are estimated by one or more methods: frequency curves, transfer of information (joint probability), regional data, paleohydrology, Bayesian and PMF groups of methods. The contemporaneous aspects of analysis of flood characteristics are related to reliability of estimation of floods of small exceedence probabilities in the range 10-2 to 10-7, whether there is an upper bound to floods and whether it is feasible to attach a probability value to probable maximum flood (PMF). To eventually answer these basic questions, three investigations are needed: (1) study of properties of the upper tail of probability distributions of floods; (2) use of regional data for drawing either the envelopes of largest floods or the curves of average largest flood characteristics for given sample sizes in the region, with probabilities attached to these envelopes or average curves; and (3) finding of the composite probability of PMF by studying the aggregated probabilities of random variables which are “maximized” in the process of computing PMP and PMF. Flood characteristics change with time due to changes in river basins. The need exists for methods of estimation of flood characteristics over periods of time of 25–100 years, particularly for planning flood mitigation measures over an extended future.

Correlation between sample first autocorrelation coefficient and extreme hydrologic runs

Abstract Differences between the annual runoff series, as the systems water supply and the annual output series, as the systems water demand, define various types of runs. The extreme runs of samples of these differences are positively correlated with the parameters of series dependence in general, and series first autocorrelation coefficient r 1 , estimated from these samples, in particular. This correlation is made between the estimated r 1 and each of the three variables of sample extreme runs. These variables are defined as summations of n longest or largest positive and longest or largest negative sample extreme runs. The resulting regression equations of r 1 versus these variables permit an alternative estimation of ϱ 1 , if this estimate is needed for any purpose. As expected, these correlations are always positive and relatively high. To show how high these correlations are, two models are used to generate samples of different sizes with various population ϱ 1 values and to study the resulting correlation: (1) first-order autoregressive normal process; and (2) dependent lognormal process, obtained by the exponential transformation of the first-order autoregressive normal process.

Covariance between subsample mean and variance as related to storage variables

Abstract The covariance, cov ( x , s 2 x ) , between mean and variance of subsamples is conceived as a single parameter which integrates the effects of asymmetrical extremes and dependence structure on storage capacity required for seasonal flow regulation. An exact expression for this covariance for the first-order autoregressive processes is derived. The use of cov ( x ,s 2 x ) for estimation of skewness is investigated by simulation for both independent and dependent stationary processes. This approach is shown to result in a lesser bias in estimated skewness than the moment estimator. The relationship between cov ( x ,s 2 x ) and the storage related variables, such as range and deficit, is also studied by simulation. It is found that cov ( x ,s 2 x ) is positively correlated with mean range and deficit for skewness smaller than 3, and negatively correlated with adjusted range. It is concluded that these storage related variables are influenced in different ways by the sampling fluctuations in the coefficients of skewness and serial correlation.

Hydrologic Forecasting for Operation

This chapter is based on the premise that both water supply and water demand of a complex water resources system contain compositions and variations of their time series, that make them conducive to hydrologic forecast. Because demand is often highly affected by climatic and hydrologic variables (precipitation, temperature, soil moisture, snowmelt, etc.), it is subject also to hydrologic forecasting techniques, similar but not identical to water supply forecast. The ensuing discussion is not concerned with the details of forecast methods; rather it stresses the interaction of the power and utility of forecasting in providing benefits for the operation of water resources systems.

Design of Objective Functions for Water Resource Systems

Specific problems in operation of complex water resources systems are basically two: (1) decisions on water releases, and (2) satisfaction of various levels of service. The first problem relates to how much water will be released from storage in a given time interval. The second problem relates to the distribution of positive or negative effects of these releases among the water related interests.