Stochastic Rational Method for Estimation of Flood Peak Uncertainty in Arid Basins: Comparison between Monte Carlo and First Order Second Moment Methods with a Case Study in Southwest Saudi Arabia

Abstract

The flood peak is commonly estimated using the rational method for the design of hydraulic structures. The method is mainly used in a deterministic context. However, there is often uncertainty in flood predictions, which should be incorporated in the design of mitigation schemes. This research proposes a methodology to cope with uncertainty in the rational method via the application of a stochastic framework. Data from 158 storms, recorded in the period 1984–1987 in 19 subbasins in the southwestern part of Saudi Arabia, were used to implement the proposed methodology. A tri-variate log-normal probability density function was used to model the joint relationship between the rational method parameters. The model considered the parameters as random variables. The uncertainty in the rainstorms was represented by intensity or depth; the uncertainty in basin delineation (due to the use of different digital elevation model resolution) was represented by the basin area; and the uncertainty in the land use/land cover was represented by the runoff coefficient. The Monte Carlo method was used to generate realizations of the peak flow and runoff volume with 95% and 99% confidence levels from the input parameters. Although the correlation between the parameters was weak, the model was capable of simulating the rational model parameters and estimating the peak flow and runoff volume relatively well, and the generated realizations fell within the confidence levels, except for a few marginal cases. The model can be used to generate peak flows and the associated confidence limits in ungauged basins from the statistics of the input parameters using the equations developed in this study.

Enhancing a Real-Time Flash Flood Predictive Accuracy Approach for the Development of Early Warning Systems: Hydrological Ensemble Hindcasts and Parameterizations

“…If radar or some other rainfall input data method (i.e., satellite remote sensing) would indeed produce more accurate results than the Thiessen polygon method, that methodological comparison might be a topic of follow-up studies. Presumably, our proposed calibration and parameter optimization methodology needs to be adjusted and modified for predictions in ungauged basins using different rainfall estimation methods, such as in [78], but the proposed hydrological ensemble calibration approach can still be analogously applied regardless of the rainfall data input method.…”

Flood adaptation impacts of blue-green infrastructure through hydrosocial framework.

“…Green space coverage in developed areas impacts the runoff volume and peak flow through pervious surface that reduce ratio of runoff coefficients. The process will involve two steps of equations based on Rational Method [39]. The rational method typically applies to drainage areas that are no greater than 200 acres (other governing bodies allow this upper limit to be as high as 640 acres).…”

Integrated Hydrological Modeling for Watershed Analysis, Flood Prediction, and Mitigation Using Meteorological and Morphometric Data, SCS-CN, HEC-HMS/RAS, and QGIS

“…Floods can be quantified in a variety of methods, including simple empirical procedures [21], the rational method [22], the flood frequency method [23], simplified conceptual models [24], multi-criteria decision analysis [25,26], and numerical and geographic information system (GIS)-based hydrodynamic modelling [7,16,27,28]. Hydrodynamic models are frequently employed in thorough flood dynamics simulations and are primarily associated with flood forecasting, mapping, and scenario analysis [29].…”