## 1. Introduction

[2] Floods are often generated by different processes in the same catchment. In parts of Western Australia, for example, floods with a return period less than 10 years are typically winter floods, whereas floods with a return period larger than 30 years tend to be summer floods despite generally drier soils in summer [*Sivandran*, 2002]. This arises due to different mechanisms of rain producing events (frontal events in winter, thunderstorms and tropical cyclones in summer), and their interaction with different flooding processes dominating in different times of the year. In Austria there also exist significant seasonal patterns of flood processes. In most of the country, the most extreme floods are summer floods, often produced by long-duration synoptic events, while smaller floods can occur throughout the year [*Merz and Blöschl*, 2003]. Differences in flood processes related to rain-fed (in summer and autumn) and snowmelt driven (spring) floods have received attention in North America and Europe [*Waylen and Woo*, 1982; *Stedinger et al.*, 1992]. *Hirschboeck* [1987] performed a detailed analysis on causative mechanisms of floods in a number of catchments in Arizona based on surface and upper weather maps [*Hirschboeck*, 1988]. This scheme was updated by *House and Hirschboeck* [1997] and simplified into three event types (tropical, convective, and frontal events). The body of work on causative mechanisms allowed *Hirschboeck* [1987] and *Alila and Mtiraoui* [2002] to examine the flood statistics for each group of events and derive hydroclimatically defined mixed distributions in flood series. *Merz and Blöschl* [2003] found significantly different flood frequency statistics for long-rain floods, short-rain floods, flash floods, rain-on-snow floods, and snowmelt floods in Austria. The need to distinguish between flood frequency curves in different months of the year, e.g., between summer and winter, or between rain-fed or snowmelt driven floods, is becoming much more critical because changes in climate and land use cannot be fully investigated without explicitly incorporating changes in the associated intra-annual (e.g., seasonal) and interannual (i.e., between year) variabilities. This is the main motivation for this paper.

[3] Traditional flood frequency analysis depends upon the existence of long periods of flood records. A recent concern with such data-driven procedures is that changes in climate and/or land uses may affect the flood frequencies, yet may not be reflected by the short records we currently have [*Franks and Kuczera*, 2002; *Sankarasubramanian and Lall*, 2003], and the consequent nonstationarities in the data record may invalidate traditional flood frequency analysis. Also, unraveling land use and climate change effects from observed flood frequency curves is notoriously difficult [*Kundzewicz*, 2003].

[4] Therefore flood frequency estimation in the future is increasingly likely to be based on a combination of traditional data-driven procedures, with increased use of rainfall-runoff models that can capture the effects of both climate and land use changes [*Blazkova and Beven*, 1997]. Derived flood frequency procedures are amenable to this kind of investigation. The derived flood frequency approach consists of the following elements: (1) a statistical model of rainfall, usually expressed in the form of a joint probability distribution of rainfall intensity and duration, including, if necessary, a correction for the effects of catchment size; (2) a deterministic rainfall-runoff model which, in turn, contains three components, namely, a runoff generation model, a runoff routing model, and a method for the accounting of antecedent catchment wetness; and (3) a mathematical framework, or “methodology”, within which the above two elements are combined together to permit the “derivation” or estimation of the probability of exceedance of a given flood magnitude, thus leading to the “derived” flood frequency curve. In previous work two alternative methodologies have been adopted for deriving the flood frequency curve. The first approach is a Monte Carlo approach where rainfall time series are generated by a stochastic rainfall model and used to drive a continuous rainfall-runoff model [*Ott and Linsley*, 1972; *Beven*, 1986; *Rahman et al.*, 2002]. From the runoff time series so generated the flood frequency curve is constructed. The second approach is a direct or analytical approach where the flood frequency curve is derived from the rainfall frequency curve using derived distribution theory [*Eagleson*, 1972; *Sivapalan et al.*, 1990; *Fiorentino and Iacobellis*, 2001]. It is only feasible when the rainfall-runoff model and the stochastic models of rainfall and antecedent conditions are simple enough for the derivations to be analytically tractable but has the advantage that the effects of the various processes can be clearly distinguished in the final set of equations. The main contribution of the derived flood frequency approach has been the ability to understand the process controls of flood frequency behavior, especially the ability to focus attention on change of dominant processes with increasing return period [*Sivapalan et al.*, 1990; *Blöschl and Sivapalan*, 1997], and therefore the ability to adapt flood estimation procedures to these dominant processes [*Jothityangkoon and Sivapalan*, 2001].

[5] Intra-annual variability in climate impacts upon the flood frequency curves in two ways: (1) seasonal and interannual variability of storm characteristics have a direct bearing on flood frequency distributions and (2) seasonality of rainfall and evapotranspiration affect the antecedent catchment conditions for individual storm events, and thus have an indirect effect on the magnitudes of the flood peaks. In spite of the widely acknowledged importance of seasonality of storm characteristics and of antecedent conditions on flood frequency these effects, to our knowledge, have never been explicitly included in any of the analytical derived flood frequency models presented in the literature. Clearly, this requires an explicit linking of derived flood frequency models with long-term water balance models, around a mathematical framework that enables the explicit inclusion of seasonality. This is the subject matter of this paper. Specifically, the aim of this paper is to explore the connection between the seasonality of floods and the seasonalities of climatic characteristics and the catchment state.

[6] The presentation of the paper will adopt the following outline. In section 2 we give examples of seasonal variability of flood frequency. We then give a mathematical presentation of the quasi-analytical derived flood frequency methodology in section 3, including a description of the way we derive annual flood frequency curves from monthly curves. In section 4 we describe the implementation of the continuous simulation or Monte Carlo approach with the same or equivalent model structures and parameters as the quasi-analytical approach, which we will use as a check of the quasi-analytical results. Section 5 is devoted to the application of the new derived flood frequency methodology to a typical catchment in Austria, its validation by comparing against results obtained using the Monte Carlo simulation approach, and the use of sensitivity analysis to gain insights into the effects of seasonality on monthly and annual flood frequency curves. Section 6 provides a discussion and the conclusions.