Academic literature on the topic 'Regional Flood Frequency Analysis Stepwise Regression Analysis Nonlinear Regression Analysis'

Abstract The log-linear regression model is one of the most commonly used models to estimate flood quantiles at ungauged sites within the regional frequency analysis (RFA) framework. However, hydrological processes are naturally complex in several aspects including nonlinearity. The aim of the present paper is to take into account this nonlinearity by introducing the generalized additive model (GAM) in the estimation step of RFA. A neighborhood approach using canonical correlation analysis (CCA) is used to delineate homogenous regions. GAMs possess a number of advantages such as flexibility in shapes of the relationships as well as the distribution of the output variable. The regional model is applied on a dataset of 151 hydrometrical stations located in the province of Québec, Canada. A stepwise procedure is employed to select the appropriate physiometeorological variables. A comparison is performed based on different elements (regional model, variable selection, and delineation). Results indicate that models using GAM outperform models using the log-linear regression as well as other methods applied to this dataset. In addition, GAM is flexible and allows for the inclusion and presentation of nonlinear effects of explanatory variables, in particular, basin area effect (scale). Another finding is the reduced effect of CCA delineation when combined with GAM.

Abstract This paper presents an approach for regional flood frequency analysis (RFFA) in the presence of nonlinearity and problematic stations, which require adapted methodologies. To this end, the projection pursuit regression (PPR) is proposed. The PPR is a family of regression models that applies smooth functions on intermediate predictors to fit complex patterns. The PPR approach can be seen as a hybrid method between the generalized additive model (GAM) and the artificial neural network (ANN), which combines the advantages of both methods. Indeed, the PPR approach has the structure of a GAM to describe nonlinear relations between hydrological variables and other basin characteristics. On the other hand, PPR can consider interactions between basin characteristics to improve the predictive capabilities in a similar way to ANN, but simpler. The methodology developed in the present study is applied to a case study represented by hydrometric stations from southern Québec, Canada. It is shown that flood quantiles are mostly associated with a dominant intermediate predictor, which provides a parsimonious representation of the nonlinearity in the flood-generating processes. The model performance is compared to eight other methods available in the literature for the same dataset, including GAM and ANN. When using the same basin characteristics, the results indicate that the simpler structure of PPR does not affect the global performance and that PPR is competitive with the best existing methods in RFFA. Particular attention is also given to the performance resulting from the choice of the basin characteristics and the presence of problematic stations.

AbstractHydrological systems are naturally complex and nonlinear. A large number of variables, many of which not yet well considered in regional frequency analysis (RFA), have a significant impact on hydrological dynamics and consequently on flood quantile estimates. Despite the increasing number of statistical tools used to estimate flood quantiles at ungauged sites, little attention has been dedicated to the development of new regional estimation (RE) models accounting for both nonlinear links and interactions between hydrological and physio-meteorological variables. The aim of this paper is to simultaneously take into account nonlinearity and interactions between variables by introducing the multivariate adaptive regression splines (MARS) approach in RFA. The predictive performances of MARS are compared with those obtained by one of the most robust RE models: the generalized additive model (GAM). Both approaches are applied to two datasets covering 151 hydrometric stations in the province of Quebec (Canada): a standard dataset (STA) containing commonly used variables and an extended dataset (EXTD) combining STA with additional variables dealing with drainage network characteristics. Results indicate that RE models using MARS with the EXTD outperform slightly RE models using GAM. Thus, MARS seems to allow for a better representation of the hydrological process and an increased predictive power in RFA.

Abstract The peak-discharge and drainage area power-law relation has been widely used in regional flood frequency analysis for more than a century. The coefficients and can be obtained by nonlinear or log-log linear regression. To illustrate the deficiencies of applying log-transformation in peak-discharge power-law analyses, we studied 52 peak-discharge events observed in the Iowa River Basin in the United States from 2002 to 2013. The results show that: (1) the estimated scaling exponents by the two methods are remarkably different; (2) for more than 80% of the cases, the power-law relationships obtained by log-log linear regression produce larger prediction errors of peak discharge in the arithmetic scale than that predicted by nonlinear regression; and (3) logarithmic transformation often fails to stabilize residuals in the arithmetic domain, it assigns higher weight to data points representing smaller peak discharges and drainage areas, and it alters the visual appearance of the scatter in the data. The notable discrepancies in the scaling parameters estimated by the two methods and the undesirable consequences of logarithmic transformation raise caution. When conducting peak-discharge scaling analysis, especially for prediction purposes, applying nonlinear regression on the arithmetic scale to estimate the scaling parameters is a better alternative.

Abstract. This study investigates the utilization of hydrological information in regional flood frequency analysis (RFFA) to enforce desired properties for a group of gauged stations. Neighbourhoods are particular types of regions that are centred on target locations. A challenge for using neighbourhoods in RFFA is that hydrological information is not available at target locations and cannot be completely replaced by the available physiographical information. Instead of using the available physiographic characteristics to define the centre of a target location, this study proposes to introduce estimates of reference hydrological variables to ensure a better homogeneity. These reference variables represent nonlinear relations with the site characteristics obtained by projection pursuit regression, a nonparametric regression method. The resulting neighbourhoods are investigated in combination with commonly used regional models: the index-flood model and regression-based models. The complete approach is illustrated in a real-world case study with gauged sites from the southern part of the province of Québec, Canada, and is compared with the traditional approaches such as region of influence and canonical correlation analysis. The evaluation focuses on the neighbourhood properties as well as prediction performances, with special attention devoted to problematic stations. Results show clear improvements in neighbourhood definitions and quantile estimates.

Regional flood frequency techniques are commonly used to estimate flood quantiles when flood data are unavailable or the record length at an individual gauging station is insufficient for reliable analyses. These methods compensate for limited or unavailable data by pooling data from nearby gauged sites. This requires the delineation of hydrologically homogeneous regions in which the flood regime is sufficiently similar to allow the spatial transfer of information. Therefore, several Regional Flood Frequency Analysis (RFFA) methods are applied to the Ceyhan Basin. Dalyrmple (1960) Method is applied as a common RFFA method used in Turkey. Multivariate statistical techniques which are Stepwise and Nonlinear Regression Analysis are also applied to flood statistics and basin characteristics for gauging stations. Rainfall, Perimeter, Length of Main River, Circularity, Relative Relief, Basin Relief, Hmax, Hmin, Hmean and H&Delta
are the simple additional basin characteristics. Moreover, before the analysis started, stations are clustered according to their basin characteristics by using the combination of Ward&rsquo
s and k-means clustering techniques. At the end of the study, the results are compared considering the Root Mean Squared Errors, Nash-Sutcliffe Efficiency Index and % difference of results. Using additional basin characteristics and making an analysis with multivariate statistical techniques have positive effect for getting accurate results compared to Dalyrmple (1960) Method in Ceyhan Basin. Clustered region data give more accurate results than non-clustered region data. Comparison between clustered region and non-clustered region Q100/Q2.33 reduced variate values for whole region is 3.53, for cluster-2 it is 3.43 and for cluster-3 it is 3.65. This show that clustering has positive effect in the results. Nonlinear Regression Analysis with three clusters give less errors which are 29.54 RMSE and 0.735 Nash-Sutcliffe Index, when compared to other methods in Ceyhan Basin.