Development of regional flood frequency analysis approaches in LH-moment framework

Abstract

Reliable estimation of design flood is crucial for planning and designing hydraulic structures, especially in ungauged or sparsely gauged locations. Regional Flood Frequency Analysis (RFFA) is a widely used approach to estimate flood quantiles at those locations by leveraging data from hydrologically similar sites. RFFA framework has been developed based on the probability weighted moments (PWMs) instead of the ordinary product moments owing to their robustness to outliers and reliable estimation. LH-moments, a combination of higher PWMs, play a crucial role in RFFA by assisting in estimation of design flood quantiles at ungauged sites within river basins. They also offer advantages over conventional L-moments in handling highly skewed peak flow distributions, making them a preferred choice for computing the design flood quantiles. This thesis has developed advanced RFFA approaches based on LH-moments framework, which offer reliable prediction of design flood estimation at ungauged locations in comparison to the conventional RFFA approaches based on L-moments framework. The major contributions from this thesis include the followings: (i) Development of LH-moment framework based RFFA to determine design floods in Krishna River Basin: LH-moments framework is generally known to characterize the upper tail of the frequency distribution for statistical analysis of events such as floods and extreme rainfall that have large return period. There is a dearth of attempts to develop LH-moment based RFFA framework for Indian catchment. In this study, LH-moment based RFFA is used to determine flood quantiles at ungauged sites corresponding to various return periods within the Krishna River basin, India. Three probability distributions, namely generalized extreme value (GEV), generalized logistic (GLO), and generalized Pareto (GPA) distribution are considered for performing RFFA. In this study. two cases are considered for RFFA: first, a single region containing all 24 gauges within the basin; and second, the division of the 24 gauges into three hydrologically similar regions based on the global K-means (GKM) clustering algorithm. The discordancy and heterogeneity measures are considered for the screening of peak flow data and checking the heterogeneity of the hydrologically similar regions, respectively. The performance assessment of the LH-moment based RFFA framework is carried out through Leave-One-Out CrossValidation (LOOCV) experiment. In first case, GEV is found to be the best-suited distribution, whereas in the second case, the GEV{GEV}[GPA] is observed as the best-fitted regional distribution for region 1{2}[3]. Overall, the analyses highlight the efficacy of the higher-order LH-moment based RFFA over the L-moment. (ii) Development of LH-moment framework based RFFA for general peak discharge distribution datasets: The index flood approach assumes that the frequency distribution of the variable is identical across sites in the region except for site specific scaling factor. In real-world scenario, this assumption may not be valid even if a region is statistically homogeneous and the regional frequency distribution is required to be identified through appropriate regional goodness-of-fit test. There is a lack of a framework for carrying out flood frequency analysis for general peak discharge distribution datasets in regional sense, i.e., the RFFA for general peak discharge distribution datasets. In this thesis, we have proposed an approach to perform RFFA for general peak discharge distribution datasets, wherein the at-site peak flood datasets are normalized with the central indicators and then transformed into normal distribution using Box-Cox transformation strategy. The proposed approach has been formulated in both L- as well as in LH-moment framework. The efficacy of the approach is demonstrated using the Monte Carlo simulation experiment and with application on datasets from real-world scenario. The outcomes of the performance measures from the simulation experiments and real-world scenario indicates that the proposed transformation-based approach provides either comparable or better estimates of design floods than CIF approach, especially in the case of mis-specification of regional distribution. (iii) Development of LH-moment framework to RFFA based on log Pearson type III distribution: The Log-Pearson type 3 (LP3/LPIII) distribution has been endorsed by the United States of Water Resources Council as a standard method for performing regional flood frequency analysis, since its robustness in accommodating a wide range of skewness in the peak flow datasets. There is lack of attempts to perform RFFA by considering LP3 as a regional distribution, especially in LH-moment framework. This study focused on formulation of parameter estimation of LP3 distribution in LH-moment framework. Subsequently, its performance in predicting design flood quantile at ungauged sites is evaluated through Monte Carlo simulation experiments and application on real-world datasets. The results from the simulation experiment reveals the better performance of LP3 distribution over the skewed distribution, especially when the return period is greater than 75 years. Performance from the real-world applicability reveals that the LP3 distribution can enhance the accuracy in estimating the design flood quantile for ungauged sites corresponding to various return periods. This research may further contribute to the broader understanding of regional flood dynamics through a reliable framework for robust flood risk assessments. (iv) Formulation of a transformation-based approach to RFFA in LH-moment framework: The final portion of the study aimed at the formulation of transformation-based approach (TA) to RFFA in LHmoment framework. The parameter estimation for five commonly used distribution in RFFA (i.e., GEV, GLO, GPA, GNO and PE3) is derived in transformed domain. The approach utilizes the location, scale, and shape parameters of a specified distribution of peak flow from original space to a known dimensionless space. Further, the formulation for location, scale and the shape parameter of GNO and PE3 distribution in LH-moment framework are also derived in original space, since their unavailability. Furthermore, a Kappa distribution-based LH-moment ratio diagram is constructed to perform regional goodness-of-fit- test. Subsequently, a Monte Carlo simulation experiment is conducted to evaluate the robustness of the developed TA over Conventional Index Flood (CIF) approach. Finally, the efficacy of the developed TA is validated through application to real-world catchment of conterminous United States, and four major river basins in South India. Results indicates that the RFFA based on LH-moment framework tends to provide reliable estimates of design flood quantiles corresponding to various return periods, in comparison to L-moment framework, in the case of both CIF and TA. Further, a significant improvement is evident when the analysis is performed by using the proposed TA in LH-moment framework. In summary, the results confirm that developed LH-moment framework based RFFA approaches have yielded significant improvement in prediction of design floods in river basins, relative to the conventional L-moment based approaches. Overall, the findings of this thesis provide valuable insights for flood risk management and infrastructure planning within river basins.