Joint Distribution of Rainfall Characteristics: Intensity, Total Depth, Spatial and Temporal Moments

2021 ◽  
Author(s):  
Roberto Quaglia ◽  
Ross Woods ◽  
Dawei Han
Keyword(s):  
Joint Distribution ◽  
Study Data ◽  
Flood Frequency ◽  
Regional Frequency Analysis ◽  
Design Flood ◽  
Ungauged Catchments ◽  
Frequency Method ◽  
Rainfall Characteristics ◽  
Temporal Moments ◽  
Vine Copula

<p>Determination of peak flow or flow hydrograph in ungauged basins can be affected by considerable degree of uncertainty. Despite the considerable efforts to overcome this challenge, current methods provide design flood estimates that are still highly uncertain in ungauged catchments, even in the UK where the gauged network is relatively dense. A possible solution may be found in stochastic approaches and more specifically in the Derived Flood Frequency method, which gives the possibility to decompose runoff response effects dictated by the dominant hydrological processes for a catchment under study. Data scarcity can be then circumvented by application of UK-specific stochastic models, from which rainfall events and their relevant features are sampled. In this work, the latter rainfall model will be presented as a joint distribution function of spatial and temporal moments of catchment rainfall, along with their Intensity and Total Depth. The marginal distributions for each rainfall characteristic are studied through the L-moment method, which was previously developed for regional frequency analysis. The multivariate distribution of these rainfall characteristics will be described through the Vine Copula method, which can account for dependence very flexibly among several variables. Parameterisation procedures still require more development to allow application over ungauged case of studies.</p>

scholarly journals A Method for Estimating the Regional Initial and Constant Loss for Design Flood Estimation in West Peninsular Malaysia

2013 ◽  
Vol 74 (2) ◽  
Author(s):  
Sazali Osman ◽  
Ismail Abustan ◽  
Rozi Abdullah
Keyword(s):  
Peninsular Malaysia ◽  
Flood Frequency ◽  
Percentage Error ◽  
Rainfall Runoff ◽  
Design Flood ◽  
Frequency Method ◽  
Flood Estimation ◽  
Common Technique ◽  
Loss Method ◽  
Regional Design

Floods are known as one of the world’s most frequent and devastating events. Techniques to predict and estimate the size of floods is depend on the availability of hydrological data. Using the conceptual of lump model, rainfall-runoff method is widely used in design flood estimation, which represents the input of rainfall and catchment characteristics such as rainfall depth, rainfall intensity, baseflow and losses. 7o calculate the catchments runoff, amount of losses shall be determine accurately by considering various source of the rainfall losses such as evaporation, inßltration, interception, depression storage and loss in groundwater recharge. In Malaysia, the common technique to estimate the hydrological losses is using initial and constant loss method. Furthermore, the value has been used in Urban Stormwater Manual for Malaysia (USMA) are adopted from the other literatures which is not represented the value from local catchment.7he objective of this study is to derive the initial and constant loss values using the data from selected local catchments in west Peninsular Malaysia. 7he calculated initial and constant loss will be further used to derive design flood discharge based on the design rainfall. An initial loss and constant loss model was examined in this study to observe the loss rate parameters in heterogeneous catchments and evaluate their signißcance as well as their potential influence on design peak floods. 7he study has been utilised the rainfall and runoff data from 113 storms over 15 catchments. 7he loss parameters were obtained from model optimi3ation using the HEC-HMS Modeling program. From the analyses, the median initial loss is 21.54mm with the standard deviation 7.85mm. 7he value shows higher than the value adopted in USMA. Meanwhile, the value for constant loss is 8.07mm which between the range of USMA. Based on the ßndings of design initial loss analyses, the values of initial loss were 49.3, 57.6, 64.1, 69.4, 73.3 and 76.6 for ARI 2,5,10,20,50 and 100, respectively. 7he percentage error between design initial loss and constant loss method and flood frequency method shows good results which are most of the percentage error less than 35%. It shows that the design initial loss and constant loss method produce reasonable accurate results when compared to the rainfall-runoff method and flood frequency method. Based on the ßndings, it can be suggested that the regional design initial loss and the constant loss rates would be able to serve reasonably well in determining catchment loss for the design purposes.

scholarly journals A New Empirical Approach to Calculating Flood Frequency in Ungauged Catchments: A Case Study of the Upper Vistula Basin, Poland

Water ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 601 ◽  
Author(s):  
Dariusz Młyński ◽  
Andrzej Wałęga ◽  
Tomasz Stachura ◽  
Grzegorz Kaczor
Keyword(s):  
Empirical Model ◽  
Catchment Area ◽  
Flood Frequency ◽  
Ungauged Catchments ◽  
Volume Determination ◽  
Statistical Verification ◽  
Observation Series ◽  
Data Estimation

The aim of the work was to develop a new empirical model for calculating the peak annual flows of a given frequency of occurrence (QT) in the ungauged catchments of the upper Vistula basin in Poland. The approach to the regionalization of the catchment and the selection of the optimal form of the empirical model are indicated as a novelty of the proposed research. The research was carried out on the basis of observation series of peak annual flows (Qmax) for 41 catchments. The analysis was performed in the following steps: statistical verification of data; estimation of Qmax flows using kernel density estimation; determination of physiographic and meteorological characteristics affecting the Qmax flow volume; determination of the value of dimensionless quantiles for QT flow calculation in the upper Vistula basin; verification of the determined correlation for the calculation of QT flows in the upper Vistula basin. Based on the research we conducted, we found that the following factors have the greatest impact on the formation of flood flows in the upper Vistula basin: the size of catchment area; the height difference in the catchment area; the density of the river network; the soil imperviousness index; and the volume of normal annual precipitation. The verification procedure that we performed made it possible to conclude that the developed empirical model functions correctly.

scholarly journals Regional flood frequency analysis of Tripura based on L-moment

2012 ◽  
Vol 4 (1) ◽  
pp. 36-41 ◽  
Author(s):  
Abhijit Bhuyan ◽  
Munindra Borah
Keyword(s):  
Frequency Analysis ◽  
Regional Growth ◽  
Growth Curves ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Ungauged Catchments ◽  
Discharge Data ◽  
Pearson Type ◽  
Regional Flood Frequency Analysis ◽  
Regional Flood Frequency

The annual maximum discharge data of six gauging sites have been considered for L-moment based regional flood frequency analysis of Tripura, India. Homogeneity of the region has been tested based on heterogeneity measure (H) using method of L-moment. Based on heterogeneity measure it has been observed that the region consist of six gauging sites is homogeneous. Different probability distributions viz. Generalized extreme value (GEV), Generalized Logistic (GLO), Generalized Pareto (GPA), Generalized Normal (GNO), Pearson Type III (PE3) and Wakebay (WAK) have been considered for this investigation. PE3, GNO and GEV have been identified as the candidate distributions based on the L-moment ratio diagram and ZDIST -statistics criteria. Regional growth curves for three candidate distributions have been developed for gauged and ungauged catchments. Monte Carlo simulations technique has also been used to estimate accuracy of the estimated regional growth curves and quantiles. From simulation study it has been observed that PE3 distribution is the robust one.

Comparison of Annual Maximum and Peaks Over Threshold Methods with Automated Threshold Selection in Flood Frequency Analysis: A Case Study for Australia

2021 ◽  
Author(s):  
Xiao Pan ◽  
Ataur Rahman
Keyword(s):  
Frequency Analysis ◽  
Flood Frequency ◽  
Distribution Functions ◽  
Flood Frequency Analysis ◽  
Annual Maximum ◽  
Threshold Selection ◽  
Peaks Over Threshold ◽  
Design Flood ◽  
Threshold Detection ◽  
Using Data

Abstract Flood frequency analysis (FFA) enables fitting of distribution functions to observed flow data for estimation of flood quantiles. Two main approaches, Annual Maximum (AM) and peaks-over-threshold (POT) are adopted for FFA. POT approach is under-employed due to its complexity and uncertainty associated with the threshold selection and independence criteria for selecting peak flows. This study evaluates the POT and AM approaches using data from 188 gauged stations in south-east Australia. POT approach adopted in this study applies a different average numbers of events per year fitted with Generalised Pareto (GP) distribution with an automated threshold detection method. The POT model extends its parametric approach to Maximum Likelihood Estimator (MLE) and Point Moment Weighted Unbiased (PMWU) method. Generalised Extreme Value (GEV) distribution using L-moment estimator is used for AM approach. It has been found that there is a large difference in design flood estimates between the AM and POT approaches for smaller average recurrence intervals (ARI), with a median difference of 25% for 1.01 year ARI and 5% for 50 and 100 years ARIs.

scholarly journals Regional analysis using the Geomorphologic Instantaneous Unit Hydrograph (GIUH) method

2014 ◽  
Vol 9 (No. 1) ◽  
pp. 25-30 ◽  
Author(s):  
M.R. Khaleghi ◽  
J. Ghodusi ◽  
H. Ahmadi
Keyword(s):  
High Efficiency ◽  
Linear Regression Analysis ◽  
Regional Analysis ◽  
Suitable Model ◽  
Rainfall Runoff ◽  
Unit Hydrograph ◽  
Design Flood ◽  
Ungauged Catchments ◽  
Northern Iran ◽  
Simulation Accuracy

The construction of design flood hydrographs for ungauged drainage areas has traditionally been approached by regionalization, i.e. the transfer of information from the gauged to the ungauged catchments in a region. Such approaches invariably depend upon the use of multiple linear regression analysis to relate unit hydrograph parameters to catchment characteristics and generalized rainfall statistics. In the present study, Geomorphologic Instaneous Unit Hydrograph (GIUH) was applied to simulate the rainfall-runoff process and also to determine the shape and dimensions of outlet runoff hydrographs in a 37.1 km<sup>2</sup> area in the Ammameh catchment, located at northern Iran. The first twenty-one equivalent rainfall-runoff events were selected, and a hydrograph of outlet runoff was calculated for each event. An intercomparison was made for the three applied approaches in order to propose a suitable model approach that is the overall objective of this study. Hence, the time to peak and peak flow of outlet runoff in the models were then compared, and the model that most efficiently estimated hydrograph of outlet flow for similar regions was determined. Statistical analyses of the models demonstrated that the GIUH model had the smallest main relative and square error. The results obtained from the study confirmed the high efficiency of the GIUH and its ability to increase simulation accuracy for runoff and hydrographs. The modified GIUH approach as described is therefore recommended for further investigation and intercomparison with regression-based regionalization methods.

scholarly journals Confidence intervals for the coefficient of L-variation in hydrological applications

2010 ◽  
Vol 14 (11) ◽  
pp. 2229-2242 ◽  
Author(s):  
A. Viglione
Keyword(s):  
Confidence Intervals ◽  
Frequency Analysis ◽  
Bootstrap Method ◽  
Flood Frequency ◽  
Point Estimation ◽  
Regional Frequency Analysis ◽  
Flood Frequency Analysis ◽  
Hydrological Variable ◽  
Regional Flood Frequency Analysis ◽  
T Distribution

Abstract. The coefficient of L-variation (L-CV) is commonly used in statistical hydrology, in particular in regional frequency analysis, as a measure of steepness for the frequency curve of the hydrological variable of interest. As opposed to the point estimation of the L-CV, in this work we are interested in the estimation of the interval of values (confidence interval) in which the L-CV is included at a given level of probability (confidence level). Several candidate distributions are compared in terms of their suitability to provide valid estimators of confidence intervals for the population L-CV. Monte-Carlo simulations of synthetic samples from distributions frequently used in hydrology are used as a basis for the comparison. The best estimator proves to be provided by the log-Student t distribution whose parameters are estimated without any assumption on the underlying parent distribution of the hydrological variable of interest. This estimator is shown to also outperform the non parametric bias-corrected and accelerated bootstrap method. An illustrative example of how this result can be used in hydrology is presented, namely in the comparison of methods for regional flood frequency analysis. In particular, it is shown that the confidence intervals for the L-CV can be used to assess the amount of spatial heterogeneity of flood data not explained by regionalization models.

scholarly journals Non-Stationary Flood Frequency Analysis Using Cubic B-Spline-Based GAMLSS Model

Water ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1867
Author(s):  
Chunlai Qu ◽  
Jing Li ◽  
Lei Yan ◽  
Pengtao Yan ◽  
Fang Cheng ◽  
...  
Keyword(s):  
Quantile Regression ◽  
Frequency Analysis ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Design Flood ◽  
Statistical Parameters ◽  
B Spline ◽  
Quantile Regression Model ◽  
Design Values ◽  
The Relationship

Under changing environments, the most widely used non-stationary flood frequency analysis (NFFA) method is the generalized additive models for location, scale and shape (GAMLSS) model. However, the model structure of the GAMLSS model is relatively complex due to the large number of statistical parameters, and the relationship between statistical parameters and covariates is assumed to be unchanged in future, which may be unreasonable. In recent years, nonparametric methods have received increasing attention in the field of NFFA. Among them, the linear quantile regression (QR-L) model and the non-linear quantile regression model of cubic B-spline (QR-CB) have been introduced into NFFA studies because they do not need to determine statistical parameters and consider the relationship between statistical parameters and covariates. However, these two quantile regression models have difficulties in estimating non-stationary design flood, since the trend of the established model must be extrapolated infinitely to estimate design flood. Besides, the number of available observations becomes scarcer when estimating design values corresponding to higher return periods, leading to unreasonable and inaccurate design values. In this study, we attempt to propose a cubic B-spline-based GAMLSS model (GAMLSS-CB) for NFFA. In the GAMLSS-CB model, the relationship between statistical parameters and covariates is fitted by the cubic B-spline under the GAMLSS model framework. We also compare the performance of different non-stationary models, namely the QR-L, QR-CB, and GAMLSS-CB models. Finally, based on the optimal non-stationary model, the non-stationary design flood values are estimated using the average design life level method (ADLL). The annual maximum flood series of four stations in the Weihe River basin and the Pearl River basin are taken as examples. The results show that the GAMLSS-CB model displays the best model performance compared with the QR-L and QR-CB models. Moreover, it is feasible to estimate design flood values based on the GAMLSS-CB model using the ADLL method, while the estimation of design flood based on the quantile regression model requires further studies.

scholarly journals An elusive search for regional flood frequency estimates in the River Nile basin

2012 ◽  
Vol 16 (9) ◽  
pp. 3149-3163 ◽  
Author(s):  
P. Nyeko-Ogiramoi ◽  
P. Willems ◽  
F. M. Mutua ◽  
S. A. Moges
Keyword(s):  
Peak Flow ◽  
Regional Growth ◽  
Growth Curves ◽  
Flood Frequency ◽  
River Nile ◽  
Nile Basin ◽  
Ungauged Catchments ◽  
Hydrological Characteristics ◽  
Record Length ◽  
Historical Flow

Abstract. Estimation of peak flow quantiles in ungauged catchments is a challenge often faced by water professionals in many parts of the world. Approaches to address such problem exist, but widely used techniques such as flood frequency regionalisation is often not subjected to performance evaluation. In this study, the jack-knifing principle is used to assess the performance of the flood frequency regionalisation in the complex and data-scarce River Nile basin by examining the error (regionalisation error) between locally and regionally estimated peak flow quantiles for different return periods (QT). Agglomerative hierarchical clustering based algorithms were used to search for regions with similar hydrological characteristics. Hydrological data employed were from 180 gauged catchments and several physical characteristics in order to regionalise 365 identified catchments. The Generalised Extreme Value (GEV) distribution, selected using L-moment based approach, was used to construct regional growth curves from which peak flow growth factors could be derived and mapped through interpolation. Inside each region, variations in at-site flood frequency distribution were modelled by regression of the mean annual maximum peak flow (MAF) versus catchment area. The results showed that the performance of the regionalisation is heavily dependent on the historical flow record length and the similarity of the hydrological characteristics inside the regions. The flood frequency regionalisation of the River Nile basin can be improved if sufficient flow data of longer record length of at least 40 yr become available.

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