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In traditional flood frequency analysis, a minimum of 30 observations is required to guarantee the accuracy of design results with an allowable uncertainty, however, there has not been a recommendation for the requirement on the length of data in NFFA (nonstationary flood frequency analysis). Therefore, this study has been carried out with three aims: (i) to evaluate the predictive capabilities of nonstationary (NS) and stationary (ST) models with varying flood record lengths; (ii) to examine the impacts of flood record lengths on the NS and ST design floods and associated uncertainties; and (iii) to recommend the probable requirements of flood record length in NFFA. To achieve these objectives, 20 stations with record length longer than 100 years in Norway were selected and investigated by using both GEV (generalized extreme value)-ST and GEV-NS models with linearly varying location parameter (denoted by GEV-NS0). The results indicate that the fitting quality and predictive capabilities of GEV-NS0 outperform those of GEV-ST models when record length is approximately larger than 60 years for most stations, and the stability of the GEV-ST and GEV-NS0 is improved as record lengths increase. Therefore, a minimum of 60 years of flood observations is recommended for NFFA for the selected basins in Norway.

Many lumped rainfall-runoff models are available but no single model can account for the uniqueness and variability of all catchments. While there has been progress in developing frameworks for optimal model selection, the process currently selects a range of model structures a priori rather than starting from the hydrological data and processes. In addition, studies on differential split sample tests (DSSTs) have focused on objective function definitions and calibration approaches. In this study, seven hydrological signatures and 12 catchment characteristics from 108 catchments around Australia were extracted for two 7-year time periods: (1) wet and (2) dry. The data was modelled using the GR4J, HBV and SIMHYD models using three objective functions to explore the relationship between model performance, catchment features and identified parameters. The hypothesis is that the hydrological signatures and catchment characteristics reflect catchment behaviour, and that certain signatures and characteristics are associated with better calibration performance. The results show that a greater percentage of catchments achieved a better calibration performance in the wet period compared to the dry period and that better calibration performance is associated with catchments that have greater cumulative flow and a steeper flow duration curve. The findings are consistent across the three models and three objective functions, suggesting that there is a bias in the studied models to wetter catchments. This study echoes the need to develop a conceptual model that can accommodate a wide variety of catchments and climates and provides a foundation to optimise and improve model selection in catchments based on their unique characteristics.

In statistical modelling, it is often of interest to evaluate non-negative quantities that capture heterogeneity in the population such as variances, mixing proportions and dispersion parameters. In instances of covariate-dependent heterogeneity, the implied homogeneity hypotheses are nonstandard and existing inferential techniques are not applicable. In this paper, we develop a quasi-score test statistic to evaluate homogeneity against heterogeneity that varies with a covariate profile through a regression model. We establish the limiting null distribution of the proposed test as a functional of mixtures of chi-square processes. The methodology does not require the full distribution of the data to be entirely specified. Instead, a general estimating function for a finite dimensional component of the model, that is, of interest is assumed but other characteristics of the population are left completely unspecified. We apply the methodology to evaluate the excess zero proportion in zero-inflated models for count data. Our numerical simulations show that the proposed test can greatly improve efficiency over tests of homogeneity that neglect covariate information under the alternative hypothesis. An empirical application to dental caries indices demonstrates the importance and practical utility of the methodology in detecting excess zeros in the data.