Abstract
Abstract. The influence of the temporal changes in lateral inflow rate on the discharge variability in stream channels is explored through the analysis of the diffusion wave equation (i.e. the linearized Saint-Venant equation). To account for variability and uncertainty, the lateral inflow rate is regarded as a temporal random function. On the basis of the spectral representation theory, analytical expressions for the covariance function and evolutionary power spectral density of the random discharge perturbation process are derived to quantify variability in stream flow discharge induced by the temporal changes in lateral inflow rate. The treatment of the discharge variance (square root of the variance) gives us a quantitative estimate of uncertainty in predictions from the deterministic model. It is found that the discharge variability of stream flow is very large in the downstream reach, indicating large uncertainty anticipated from the use of the deterministic model. A larger temporal correlation scale of inflow rate fluctuations, representing more temporal consistency of fluctuations in inflow rate around the mean, introduces a higher variability in stream flow discharge.
Highlights
Surface runoff originates from precipitation intensities exceeding the infiltration capacity of the surface (e.g. Duan et al, 1992; Sivakumar et al, 2000; Ruiz-Villanueva et al, 2012; Valipour, 2015). This process may result in lateral inflow to nearby stream channels
Understanding and quantification of the influence of inflow process on stream flow discharge is essential for water resource planning and management
QM is considered to be a temporally correlated stationary random field. It is apparent from Eq (2) that the last two terms associated with the lateral inflow are introduced as the sources of fluctuations in stream flow discharge and treated here as temporally correlated stochastic processes
Summary
Surface runoff originates from precipitation intensities exceeding the infiltration capacity of the surface (e.g. Duan et al, 1992; Sivakumar et al, 2000; Ruiz-Villanueva et al, 2012; Valipour, 2015). Significant lateral inflows may contribute to streams during storm-runoff periods when stream reaches are of large lateral watershed areas or upslope accumulated areas (Jencso et al, 2009). Understanding and quantification of the influence of inflow process on stream flow discharge is essential for water resource planning and management Natural variability, such as significant variability of rainfall events on both temporal and spatial scales The non-stationary spectral techniques are employed to obtain closed-form solutions for quantifying the discharge variability in stream channels These solutions provide variance relations for flow discharge, and thereby allow for assessing the impact of statistical properties of lateral inflow rate process on the discharge variability. To the best of our knowledge, the issue on quantifying the effect of temporal variation of lateral inflow on the stream flow variability using non-stationary spectral techniques so far has not been addressed. It is hoped that the proposed approach and our findings obtained in this study are useful for further research in this area
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