A multistate first-order Markov model for modeling time distribution of extreme rainfall events

Abstract

The time distribution of extreme rainfall events is a significant property that governs the design of urban stormwater management structures. Accuracy in characterizing this behavior can significantly influence the design of hydraulic structures. Current methods used for this purpose either tend to be generic and hence sacrifice on accuracy or need a lot of model parameters and input data. In this study, a computationally efficient multistate first-order Markov model is proposed for use in characterizing the inherently stochastic nature of the dimensionless time distribution of extreme rainfall. The model was applied to bivariate extremes at 10 stations in India and 205 stations in the United States (US). A comprehensive performance evaluation was carried out with one-hundred stochastically generated extremes for each historically observed extreme rainfall event. The comparisons included: 1-h (15-min); 2-h (30-min); and, 3-h (45-min) peak rainfall intensities for India and (US) stations, respectively; number of first, second, third, and fourth-quartile storms; the dependence of peak rainfall intensity on total depth and duration; and, return levels and return periods of peak discharge when these extremes were applied on a hypothetical urban catchment. Results show that the model efficiently characterizes the time distribution of extremes with: Nash–Sutcliffe-Efficiency > 0.85 for peak rainfall intensity and peak discharge; < 20% error in reproducing different quartile storms; and, < 0.15 error in correlation analysis at all study locations. Hence the model can be used to effectively reproduce the time distribution of extreme rainfall events, thus increasing the confidence of design of urban stormwater management structures.

Quality Assessment of Small Urban Catchments Stormwater Models: A New Approach Using Old Metrics

“…As mentioned in Section 2.1, most of the NSE values reported in the calibration of hydrological or hydraulic urban drainage models range from 0.5 to 0.9, with most being greater than 0.7 [2,7,10,20,22,[46][47][48][50][51][52][53]. However, NSE values above 0.95 are also reported [1,53,55]. 5.2.2.…”

“…It is important to note that the proximity of the values of NSE, KGE and r 2 to optimal values is higher than in most cases in the literature and may derive from the approach applied in this work. As mentioned in Section 2.1, most of the NSE values reported in the calibration of hydrological or hydraulic urban drainage models range from 0.5 to 0.9, with most being greater than 0.7 [2,7,10,20,22,[46][47][48][50][51][52][53]. However, NSE values above 0.95 are also reported [1,53,55].…”

“…In urban catchments, important rainfall events last a few hours or even minutes, and therefore the time step of measurement records is usually only of a few minutes. The urban drainage literature reports NSE values from the calibration of hydrologic or hydraulic models, normally between 0.5 and 0.9 [2], most of them being greater than 0.7 [7,10,20,22,[46][47][48][50][51][52][53]. However, in some cases, NSE values above 0.95 are reported [1,53,55], while in other specific cases, usually for water quality parameters, very low values, close to zero, are considered as acceptable [9].…”

“…Obviously, in urban drainage, graphical and statistical techniques have always been applied to model calibration and evaluation, although the generalized use of aggregated efficiency metrics, such as the Nash-Sutcliffe coefficient and the Kling-Gupta coefficient [37], is more recent (e.g., [46][47][48][49][50][51][52][53][54][55]).…”