## 1. Introduction

[2] A general challenge in the field of hydrological modeling is model structure identification [*Dunn et al.*, 2008]. There are several practical criteria which may be applied for selecting a model structure, for example, a model which needs no more than the available data and produces the required output; a model with which the modeler is familiar and which has a history of working well; a model which, after estimation of parameter values, seems to perform satisfactorily on the catchment under investigation or on an analog catchment; or a model of suitable complexity so that uncertainty in parameter values is minimized. In practice, for any application, normally only one or perhaps a few readily available model structures are considered without using a rigorous selection process, and consequently, many potentially better models are overlooked. It is commonly noted that ideally, the search for the optimal model structure should be approached more systematically, and the development of identification procedures has received significant attention from hydrological modelers [e.g., *Wagener et al.*, 2003; *Young*, 2003; *Lee et al.*, 2005; *Kuczera et al.*, 2006; *Lin and Beck*, 2007; *Liu and Gupta*, 2007; *Son and Sivapalan*, 2007; *Clark et al.*, 2008; *Fenicia et al.*, 2008; *Bulygina and Gupta*, 2009; *Reichert and Mieleitner*, 2009].

[3] A common model identification procedure is based on developing prior hypotheses about hydrological processes in the catchment under study, conceptualizing these into a numerical model, and testing the performance (usually against measurements of flow from the catchment outlet) and, if performance is unacceptable, then rejecting and renewing the hypothesis, proposing a new model, and so on. This may be called the “hypothetico-deductive” approach [*Young*, 2003]. A feature of this approach is that the prior range of potentially relevant processes may be wide, leading to comprehensive, highly parameterized, highly uncertain, “physics-based” models [*Beven and Freer*, 2001]. While this type of model has a role in speculative scenario analysis [e.g., *Jackson et al.*, 2008], it does not easily allow for the identification of the dominant modes of response that are most valuable for developing conceptual understanding and for uncovering behavior that was unexpected a priori.

[4] An alternative procedure for model structure identification is the inductive, data-based mechanistic (DBM) approach, which has developed over many years from its original conception [*Young*, 1978] to the first use of the name DBM by *Young and Lees* [1993]. Its initial application to rainfall-flow modeling [e.g., *Young*, 1974, 1993; *Whitehead et al.*, 1976; *Young and Beven*, 1994] has led to continued use for this purpose over a number of years [e.g., *Young*, 2001, 2003; *Young et al.*, 2007; *Taylor et al.*, 2007].

[5] The DBM approach aims to impose minimal prior constraints on the model and to evolve the model through the assimilation and analysis of measured data. By relying as much as possible on information in the measurements, such an ideology minimizes the subjectivity in hypothesis making, and by seeking the simplest possible model structures supported by the data (i.e., parsimony), the approach aims to minimize the risk of accepting wrong, overparameterized models and seeks to isolate the few dominant modes of response that dictate the dynamic behavior of the system [*Young and Ratto*, 2009, 2011]. Recognizing that any set of hydrological measurements gives an incomplete picture of the physical system, a range of possible response modes may well be omitted with such an approach, which is dependent on the information content in the data. It follows that a data-based model should not be used to extrapolate far beyond the realm of the measurements on which it is based. However, increased confidence in predictions and increased applicability of the model for exploring scenarios may be justified if the model has physical characteristics that relate well to physical processes being investigated, despite its largely empirical origin.

[6] The DBM approach aims to identify statistically optimal yet physically plausible models. It is normally based on statistical identification of linear or nonlinear transfer functions and the subsequent decomposition of these transfer functions into models that may have a physical interpretation, using algorithms available in the CAPTAIN Toolbox for Matlab (the fully functional CAPTAIN Toolbox for Matlab can be downloaded from http://www.es.lancs.ac.uk/cres/captain/ and is available for use, without a license, for 3 months). Only models that are considered to perform well, are statistically well defined and parsimonious, and have an acceptable physical interpretation are accepted. The identified structure may then be used in a number of ways: for example, the assessment of conceptual models [*Ratto et al.*, 2007], real-time forecasting [*Young*, 2002; *Romanowicz et al.*, 2006], identification of spatial signals in response [*McIntyre and Marshall*, 2010], and providing links with reduced-order models that are used in the “emulation” of associated physically based models [*Young and Ratto*, 2009, 2011].

[7] This paper describes the application of the DBM modeling approach to identify nonlinearity in the rainfall-flow relationship and the subsequent attempt to infer a conceptual model on the basis of the DBM modeling results. As opposed to previous DBM applications to rainfall-flow modeling, which have used hourly to daily data, this study uses 10 min resolution measurements of rainfall and of flow in two parallel flow pathways. It is proposed that because of the small spatial scale in this case, the rainfall measurements represent the catchment average rainfall more precisely than typical DBM applications where there is significant noise in the rainfall inputs associated with spatial sampling error. With this “low-noise” rainfall, along with dual-pathway flow data, we are able to extract more information about nonlinear processes than has previously been achieved using DBM modeling, including internal routing nonlinearity, rather than just nonlinearity in the effective rainfall input.