## 1. Introduction

[2] The concept of flood frequency hydrology [*Merz and Blöschl*, 2008a, 2008b] highlights the importance of using a maximum of hydrologic information from different sources and a combination based on hydrological reasoning. In their framework, *Merz and Blöschl* [2008a, 2008b] propose to compile flood peaks at the site of interest plus three additional types of information: temporal, spatial, and causal information.

[3] Temporal information expansion is directed toward collecting information on the flood behavior before (or after) the period of discharge observations (systematic data period). Spatial information expansion is based on using flood information from neighboring catchments to improve flood frequency estimates at the site of interest. Causal information expansion analyzes the generating mechanisms of floods in the catchment of interest. For each of these types of information expansion, methods have been proposed in the literature. Formal methods exist on combining historical flood data (from flood marks and archives) and possibly paleofloods with available flood records [e.g., *Leese*, 1973; *Stedinger and Cohn*, 1986; *Cohn et al*., 1997; *O'Connell et al*., 2002; *England et al*., 2003; *Reis and Stedinger*, 2005; *Benito and Thorndycraft*, 2005], which would be considered temporal information expansion. Methods of regional flood frequency analysis [e.g., *Dalrymple*, 1960; *Cunnane*, 1988; *Tasker and Stedinger*, 1989; *Bobée and Rasmussen*, 1995; *Hosking and Wallis*, 1997; *Merz and Blöschl*, 2005] would be considered spatial information expansion. Finally, the derived flood frequency approach [e.g., *Eagleson*, 1972; *Kurothe et al*., 1997; *Fiorentino and Iacobellis*, 2001; *Sivapalan et al*., 2005] or, more generally, rainfall-runoff modeling [e.g., *Pilgrim and Cordery*, 1993; *Wagener et al*., 2004] would be considered causal information expansion.

[4] As discussed in *Merz and Blöschl* [2008b], it is vital to account for the respective uncertainties of the various pieces of information when combining them. In local flood statistics, a range of estimates may result from a reasonable fit of several distributions to the observed data or by accounting for the uncertainty associated with the estimated parameters of those distributions. Historical flood data may only allow us to give a range of estimates owing to large uncertainties. Spatial information may lead to a range of estimates when using several regionalization schemes or parameters of the regionalization schemes all of which may be consistent with the regional information. Causal information may result in a range of estimates due to using different methods, different data, and uncertainty in the expert judgment. In *Merz and Blöschl* [2008b], the final estimate was obtained by expert judgment, considering the relative uncertainties of the component sources of information [see also *Gutknecht et al*., 2006].

[5] The present paper is a follow up of *Merz and Blöschl* [2008a, 2008b] where, instead of reasoning in terms of ranges of estimates, we account for the uncertainty inherent to the different sources of information using the Bayesian framework. Bayesian methods provide a computationally convenient way to fit frequency distributions for flood frequency analysis by using different sources of information as systematic flood records, historical floods, regional information, and other hydrologic information along with related uncertainties (e.g., measurement errors). They also provide an attractive and straightforward way to estimate the uncertainty in parameters and quantiles metrics.

[6] In flood hydrology, Bayesian methods have been used often for pieces of information such as historic floods [e.g., *Stedinger and Cohn*, 1986; *O'Connell et al*., 2002; *Parent and Bernier*, 2003a; *Reis and Stedinger*, 2005; *Neppel et al*., 2010; *Payrastre et al*., 2011], regional information [e.g., *Wood and Rodriguez-Iturbe*, 1975; *Kuczera*, 1982, 1983; *Madsen and Rosbjerg*, 1997; *Fill and Stedinger*, 1998; *Seidou et al*., 2006; *Ribatet et al*., 2007; *Micevski and Kuczera*, 2009; *Gaume et al*., 2010], and less frequently for other information such as, for example, expert opinion [e.g., *Kirnbauer et al*., 1987; *Parent and Bernier*, 2003b]. In the literature, there are examples in which more than one piece of additional information was used in a Bayesian analysis. For example, *Vicens et al*. [1975] investigate information expansion from regional information (through regression models) or expert judgment (causal information from precipitation characteristics) but do not combine the two together. *Martins and Stedinger* [2001] use historical information jointly with the generalized maximum likelihood method, which can be thought as regional (or expert) information expansion. The aim of this paper is to illustrate by example how all three pieces of information (Figure 1, top row) can be combined in a Bayesian analysis and to assess the sensitivity of the final flood estimate to the assumptions involved. Obviously, there may be applications, where not all three types of information expansion (temporal, spatial, and causal) can be provided, e.g., no historic flood data and/or regional studies are available; so, we test the effect of each piece of information on the flood estimates separately.

[7] The sensitivity of the flood estimate to the flood peak sample at hand is also assessed by comparing two cases in a study catchment where a very large flood has occurred. In the first case, we assume that only the information before the big flood is available to mimic the situations where no large floods have been observed but may occur. In the second case, we include the large flood.

[8] The information expansion used in this study is not only diverse in terms of the temporal, spatial, and causal character of the additional information but also in the qualitative character of the information (Figure 1, bottom row): (1) additional data, (2) full information or, and (3) partial information on the prior distribution of parameters of the selected statistical model. In the example presented hereafter, historical floods are used as additional data; regional information provides an estimate of the full distribution of the model parameters, while the estimate with uncertainty of one flood peak quantile, obtained through expert judgment from a rainfall-runoff modeler, constitutes partial information on the model parameters. This may differ in other applications, where, e.g., spatial information expansion could provide only partial information while causal information expansion could provide full information on the prior distribution of the parameters of the selected statistical model.