## 1 Introduction  
Floods are probably the most frequently recurring natural phenomenon affecting society (human and goods) in terms of space and time, regardless of their geographical location or socioeconomic development as shown by the data collected by the International Disasters Database for the period 1900-2018 [1]. This is the main reason why flood risk management has become an essential tool from both an economic and a social perspective, with the main objective of reducing their associated losses. Analyses of economic damage are always easier than those of social damage, due to the not-easily-valuable prize of human life. Assessing direct tangible damages (those direct damages resulting from the physical contact of floodwater with property and its contents, and the most common ones), economic flood losses have been increasing throughout the past half-century. In the last decade (2008-2018), economic losses associated with floods exceeded USD 35 billion [1] and, as an example within this period, flood losses exceeded USD 19 billion in 2012 alone [2; 3; 4]. Clearly, any assessment of such flood risks must commence with an evaluation of the magnitude of peak flow events with particular return periods. Management of flood risk then proceeds by setting some design recurrence interval that drainage network and urban water systems must be able to deal with. However, an evaluation of peak flow values is not an easy task, due to the uncertainty associated with the limited data availability from gauge stations. Thus, even if there are data series of maximum annual flow with lengths greater than 30 records, a value considered sufficiently long by [PERSON] et al. [5] for the application of the cumulative probability distribution function (CDF) to the annual maxima series, the representativeness of this time series with respect to the global behaviour of the peak flow variable is limited. This lack of knowledge causes the existence of the so-called epistemic uncertainty, resulting from imperfect knowledge of the system (e.g., [6; 7; 8]), or from simplifications associated with the selected modelling approach and parametrizations. Due to this limited knowledge, the use of a probabilistic approach to flood hazard mapping should be preferred to deterministic ones for at least three main reasons [9; 10; 11]: (1) hydrological and hydraulic assessments are always affected by uncertainty; (2) a correct representation of the results of a hydraulic analysis should also quantify its associated uncertainty, and this goal only can be accomplished within a probabilistic framework; and (3) the end users (stakeholders and decision makers) can only guide and support the correct definition of flood mitigation strategies under the best knowledge of flood hazard and risk. These probabilistic maps try to delimitate the uncertainty in flood hazard analysis, which could be related to many variables. Many previous studies analysed the effect of uncertainty associated with the roughness surface (Manning's \(n\) value) of hydraulic models (e.g., [5; 12; 13; 14; 15]). Additionally, other studies (e.g., [5; 16; 17; 18; 15]) analysed the uncertainty in upstream and/or downstream boundary conditions. Other authors considered additional uncertainties in flood hazard by including extreme value statistics [19; 20; 21], in many cases, by relating the changes in rainfall or flow results that may occur as a result of climate change (e.g., [22; 23; 24; 25; 26]). The importance of an uncertainty analysis in flood risk management was pointed out previously [7; 27] in order to understand the implications for decision makers of limited data availability, model uncertainties, or other uncertainty sources. Monte Carlo simulations (MC) as a technique to reduce uncertainty in flood hazard analyses have been widely used. Previous studies have used MC methods (e.g., [17; 19; 27; 28; 29]) to analyse all variables: surface roughness, boundary conditions, and return period as flow frequency variable.