## 1. Introduction

[2] Conceptual or mechanistic models are developed as mathematical representations of the underlying mechanisms governing the modeled processes based on available scientific knowledge or hypotheses [*Swartzman and Kaluzny*, 1987]. Therefore such models are more suited to Earth systems science applications, such as developing quantitative and scientific understanding of Earth systems in terms of components and processes or making informed decisions regarding long-term management of these systems [*Wainwright and Mulligan*, 2004], compared with purely empirical models [*Box et al.*, 1978; *Beven*, 1989]. Conceptual models are also easier to interpret and extend by incorporating additional information. However, such models are not completely mechanistic and necessarily simpler than the real system due to constraints such as the availability of scientific knowledge, data, and computational resources [*Oreskes et al.*, 1994; *Ellner et al.*, 1998; *Kendall et al.*, 1999; *Turner et al.*, 2001]. The simplifications in the model, natural variability in system response, and measurement errors lead to mismatches between modeled and observed responses. For most applications, the mismatches are minimized by estimating the model parameter values through calibration [*Klemeš*, 1986; *Janssen and Heuberger*, 1995; *Sorooshian and Gupta*, 1995]. However, uncertainties inherent in such estimation processes are traditionally not quantified. Lack of this information compromises the ability to statistically test hypotheses, compare model structures for suitability for specific applications, compare parameter values for different systems, or provide an estimate of expected errors in the predictions obtained using the calibrated model.

[3] Relatively recently, the above weakness in traditional model calibration has been recognized and various methodologies have been proposed for uncertainty estimation of conceptual hydrologic models [e.g., *Kuczera*, 1983; *Beven and Binley*, 1992; *Gupta et al.*, 1998; *Kuczera and Parent*, 1998; *Campbell et al.*, 1999; *Krzysztofowicz*, 1999; *Bates and Campbell*, 2001; *Thiemann et al.*, 2001; *Engeland and Gottschalk*, 2002; *Balakrishnan et al.*, 2003; *Samanta and Mackay*, 2003; *Vrugt et al.*, 2003a, 2003b; *Montanari and Brath*, 2004]. In the present study, we use a simple Bayesian framework to fit a conceptual transpiration model (section 3) to observed transpiration data (section 5) and analyze the uncertainties associated with its parameters and predictions to address whether the combined effect of uncertainties due to the model structure, parameter values, and errors in measurements can adequately be estimated, along with a quantified and realistic estimate of prediction uncertainty, by a simple additive, independent, and normally distributed error model. Therefore the emphasis of the analysis was on checking for deviations from the above assumption and evaluating the ability of the conceptual model to explain the data under this assumption, which are important in the deduction step of the iterative data-induction/model-deduction sequence of model development [*Box*, 2001]. The transpiration data used here were derived from sap flux measurements on individual trees, while most existing uncertainty analyses of conceptual transpiration models are at larger scales [e.g., *Franks and Beven*, 1997; *Franks et al.*, 1999; *Gupta et al.*, 1999; *McCabe et al.*, 2005]. The methodology employed here is similar in principle to the methodologies used to analyze streamflow and rainfall-runoff models in a number of other studies, but it differs in certain assumptions and details of analysis. A brief discussion of this methodology, in the context of other methodologies, is presented in section 2 with technical details of implementation presented in section 4.