This technical note presents a comparison of cluster-based point rainfall models using the historical hourly rainfall data observed between 1949 and 1976 at Denver, Colorado. The Denver data are used to analyze the performance of three classes of models, namely, the Bartlett-Lewis model, the geometric Neyman-Scott model and the Poisson Neyman-Scott model. The original formulation of the structure of each model, as well as the modified description developed in order to improve the zero depth probability, is considered in this study. Rodriguez-Iturbe et al. (1987a) concluded that it is unlikely that empirical analysis of rainfall data can be used to choose between the Bartlett-Lewis model and the Neyman-Scott model. In a subsequent paper, Rodriguez-Iturbe et al. (1987b) argued that the choice of the distribution of the number of cells per storm for the Neyman-Scott model, either geometric or Poisson, has no general bias effect on the stochastic structure. Some investigators (e.g., Burlando and Rosso, 1991), however, reported results contradictory to those of the previous authors. In light of these observations this note investigates the performance of the cluster-based models. For the Denver data the geometric Neyman-Scott model yields better results compared to the Poisson Neyman-Scott model. Moreover, the Bartlett-Lewis model is shown to be very sensitive to the sets of moment equations used in the parameter estimation. This sensitivity is not observed in the Neyman-Scott scheme and is believed to be a drawback for applying the Bartlett-Lewis model in hydrologic simulation studies

Abstract. Climate change is one of the biggest challenges currently faced by society, with an impact on many systems, such as the hydrological cycle. To locally assess this impact, Regional Climate Model (RCM) simulations are often used as input for hydrological rainfall-runoff models. However, RCM results are still biased with respect to the observations. Many methods have been developed to adjust these biases, but only during the last few years, methods to adjust biases that account for the correlation between the variables have been proposed. This correlation adjustment is especially important for compound event impact analysis. As a simple example of those compound events, hydrological impact assessment is used here, as hydrological models often need multiple locally unbiased input variables to ensure an unbiased output. However, it has been suggested that multivariate bias-adjusting methods may perform poorly under climate change conditions because of bias nonstationarity. In this study, two univariate and three multivariate bias-adjusting methods are compared with respect to their performance under climate change conditions. To this end, the methods are calibrated in the late 20th century (1970–1989) and validated in the early 21st century (1998–2017), in which the effect of climate change is already visible. The variables adjusted are precipitation, evaporation and temperature, of which the former two are used as input for a rainfall-runoff model, to allow for the validation of the methods on discharge. Although not used for discharge modelling, temperature is a commonly-adjusted variable in both uni- and multivariate settings and therefore important to take into account. The methods are also evaluated using indices based on the adjusted variables, the temporal structure, and the multivariate correlation. For precipitation, all methods decrease the bias in a comparable manner. However, for many other indices the results differ considerably between the bias-adjusting methods. The multivariate methods often perform worse than the univariate methods, a result that is especially notable for temperature and evaporation. As these variables have already changed the most under climate change conditions, this reinforces the opinion that the multivariate bias-adjusting methods are not yet fit to cope with nonstationary climate conditions. Although the effect is slightly dampened by the hydrological model, our analysis still reveals that, to date, the simpler univariate bias-adjusting methods are preferred for assessing climate change impact.

Abstract. Climate change is one of the biggest challenges currently faced by society, with an impact on many systems, such as the hydrological cycle. To assess this impact in a local context, regional climate model (RCM) simulations are often used as input for rainfall-runoff models. However, RCM results are still biased with respect to the observations. Many methods have been developed to adjust these biases, but only during the last few years, methods to adjust biases that account for the correlation between the variables have been proposed. This correlation adjustment is especially important for compound event impact analysis. As an illustration, a hydrological impact assessment exercise is used here, as hydrological models often need multiple locally unbiased input variables to ensure an unbiased output. However, it has been suggested that multivariate bias-adjusting methods may perform poorly under climate change conditions because of bias nonstationarity. In this study, two univariate and four multivariate bias-adjusting methods are compared with respect to their performance under climate change conditions. To this end, a case study is performed using data from the Royal Meteorological Institute of Belgium, located in Uccle. The methods are calibrated in the late 20th century (1970–1989) and validated in the early 21st century (1998–2017), in which the effect of climate change is already visible. The variables adjusted are precipitation, evaporation and temperature, of which the former two are used as input for a rainfall-runoff model, to allow for the validation of the methods on discharge. Although not used for discharge modeling, temperature is a commonly adjusted variable in both uni- and multivariate settings and we therefore also included this variable. The methods are evaluated using indices based on the adjusted variables, the temporal structure, and the multivariate correlation. The Perkins skill score is used to evaluate the full probability density function (PDF). The results show a clear impact of nonstationarity on the bias adjustment. However, the impact varies depending on season and variable: the impact is most visible for precipitation in winter and summer. All methods respond similarly to the bias nonstationarity, with increased biases after adjustment in the validation period in comparison with the calibration period. This should be accounted for in impact models: incorrectly adjusted inputs or forcings will lead to predicted discharges that are biased as well.

Interactive comment on "Impact of bias nonstationarity on the performance of uni-and multivariate bias-adjusting methods" by Jorn Van de Velde et al.Jorn Van de Velde et al.

General comments In their contribution, Schmith et al. (2020) discuss the robustness of different bias-adjusting methods for (sub)daily rainfall extremes. This yields interesting results and strong links with the context of convection-permitting models and emergent constraints. Yet, there are some aspects about whom I'd like a deeper discussion. The first aspect is the practical use of this study. This is foremost linked with the choice of bias-adjusting methods. Although the use of return periods is perfectly justified from a hydrological point of view, I've seen few studies that actually use bias adjustment directly on the return periods. As such, I'd like to see a larger discussion on the choice of bias-adjusting methods. Given a well-justified choice, I understand the use of these C1 HESSD