Rainfall-runoff models are widely used to estimate design flood hydrographs. The estimated flood hydrograph is then used to mitigate the cost and risk of flooding through, for instance, the design of flood mitigation structures or floodplain management strategies. Therefore, a range of mathematical models (including rainfall-runoff models) has been developed to improve the accuracy of design flood estimates and ensure the optimum design and management of infrastructure; for example, the Catchment Model [1], the Soil Conservation Service (SCS) Curve Model [2], and Hydrologic Engineering Centre (HEC)-1 [3] model. The relative accuracy of each model, however, is dependent on several factors, such as its intended purpose, data availability, catchment characteristics, desired accuracy, budget, and time constraints [4,5,6,7].

Rainfall-runoff models have a long history of being used for flood risk assessment, ranging from the classical rational method [8] to the modern physically based distributed models [9,10]. These models primarily seek to generate streamflow from rainfall data, which can be categorized into a few broad groups: (i) empirical black-box type models based on the nonlinear relationship between inputs and outputs, such as the SCS Curve Number Model [2]; (ii) conceptual models based on the equations that represent water storage in catchment, such as the Topography-based Hydrological Model (TOPMODEL) [11]; and (iii) physical models based on the physical laws and equations related to the hydrologic processes, such as the “Model Based and Incremental Knowledge Engineering” (MIKE)-Topography-based Hydrological Model (SHE) [12].

The rainfall-runoff models in the second group (conceptual models) are widely used for flood modelling purposes, mainly because of their flexibility and simplified governing equations [5]. These models provide the conceptual idea of the behaviors in a catchment and can be implemented when computational time and data are limited; typically, either on a continuous basis or event based. Continuous simulation techniques, for instance, the “Identification of unit Hydrographs And Component flows from Rainfall, Evaporation and Streamflow data” (IHACRES) [13], Continuous Simulation Systems (CSS) [14], and the Australian Water Balance Model (AWBM) [15], are theoretically advanced; however, these require a considerable amount of data (spatially and temporally) to calibrate the model meaningfully, particularly for larger catchments with complex hydro-climatic characteristics [16].

Conversely, event-based conceptual models, being either lumped (e.g., the initial loss–continuing loss (IL-CL) and initial loss–proportional loss (IL-PL) models) or distributed (e.g., the probability distributed model (PDM) [17], TOPMODEL [11], Xinanjiang model [18], and the soil water balance model (SWMOD) [19]), conceptualize the capacity of a model to approximate the catchment runoff response in a simplistic manner but with reasonable accuracy, often by ignoring the spatial variability of the model inputs and land characteristics. However, distributed conceptual models (unlike lumped conceptual models) account for the variability with regards to both time and space throughout the duration of a rainfall event, hence they require a substantial volume of catchment and climatic data. For instance, the Xinanjiang model (commonly used in China) uses a cumulative distribution function; similarly, the PDM model (widely applied in the UK) and the SWMOD model (used in Australia) also use a probability distribution function, to describe the spatial heterogeneity in soil storage capacities across a catchment.

Both the continuous and the event-based approaches have been applied to a range of catchments (gauged and ungauged) by many hydrologists worldwide with varying degrees of success, but the selection of an appropriate model is often difficult as there is a lack of objective comparison using standard datasets across the competing models [10,14,16,20,21].

In Australia, rainfall-runoff modelling for design flood estimation in general is dominated by the lumped event-based conceptual approaches [22] as there are limited data available across much of Australia for model calibration and verification, as well as a number of models developed specifically for Australian conditions having different combinations of loss function (representing infiltration, evaporation, interception, etc.) and transfer function (representing various runoff attenuation mechanisms).

There have been significant developments and applications of event-based conceptual rainfall-runoff models in Australia, in particular for the gauged catchments [23], with varying degrees of success, but there is a lack of systematic review of these developments. Hence, the motivation for this paper is to review the rainfall-runoff modelling practices for design flood estimation in the context of Australia with a special focus on event-based conceptual models. Four lumped event-based rainfall-runoff models are considered in this study, which are Runoff Routing Burroughs (RORB) [24], the Watershed Bounded Network Model (WBNM) [25], the Runoff Analysis and Flow Training System (RAFTS) [26], and the Unified River Catchment Simulator (URBS) [27]. Although other conceptual models could have been included in this review, only four models are covered given their extensive use throughout Australian catchments. The RORB and WBNM are widely used in rural applications, while the RAFTS model is generally more suitable for complex urban catchments. URBS has been used for flood forecasting more frequently than RORB, WBNM, and RAFTS.

While it is not practically possible to review all aspects of rainfall-runoff modelling, we attempt to cover comparative strengths and weaknesses of these models, the major routing processes, rainfall losses, and the aspects of regionalization to promote their applications to ungauged catchments. There has been limited research on comparing and contrasting these four widely used runoff routing models in Australia. Since the publication of the fourth edition of Australian Rainfall and Runoff (ARR) in 2019, the capability of these models to implement Monte Carlo simulation has become an important consideration since this is the currently recommended method of design hydrograph simulation in Australia. It is expected that this review will promote a better understanding of the model differences, including their practical applications, recent developments, and future enhancements such as consideration of climate change impacts on simulated design hydrograph. Hence, this paper is intended to serve as a key reference for commonly used event-based conceptual rainfall-runoff models in Australia for design flood estimation.