Introduction

One of the core components of flood risk management decision support system is the simulation of rainfall and runoff in flood prone areas. Accurate runoff modelling is becoming increasingly important for reliable decision support in the context of water resource management (Zang et al., 2009). Most of the studies on these problems adopt one of the two main broad techniques, which are either hydrologic or hydraulic techniques (Smith, 1994) or a coupling of the two (Francisco et al., 1998).

According to Abbott and Refsgaard (1996) hydrological models, including rainfall and runoff models, can be classified into deterministic and stochastic types. In deterministic models, a single set of input values and a single parameter set are used to generate a single set of outputs. In stochastic models, parameters are used to represent statistical distributions. Model parameters are normally generated by fitting measured data into a certain distribution. The output sets of a stochastic model are normally ranges of values, each derived from different combinations of the inputs and parameters. Each range associated with a probability of statistical certainty.

Singh (1995), on the basis of how physically processes are represented in models, classified the models into 1) empirical, regression or “black-box” models. 2) conceptual-empirical models and 3) physical based or process based models.

The empirical, regression or “black-box” models simply calibrate the relationship between rainfall and the output runoff. They do not attempt to represent the basic processes that really describe the mechanism of the relationship.

In conceptual-empirical models, the basic processes in rainfall runoff modelling such as interception, infiltration, evaporation, surface and subsurface runoff are described to

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some extent. However, the description of these processes are essentially calibrated input- output relationships based on the collected data, formulated to mimic the functional behaviour of the process in question.

Physically based or process based models depend on the fundamental physics and governing equations that describe the real physical processes to model the relationship between rainfall and runoff e.g. the process of water flow over and through soil and vegetation. They are intended to minimise the need for calibration by using relationships in which the parameters are, in principle, measurable physical quantities.

The selection of the model for use depends on a range of conditions such as the type of problem, required levels of accuracy, time constraints, data availability, usefulness of the model in terms of communication to users and the ease of use. All of the considerations mentioned above are useful to consider when answering the following two questions: “What is the appropriate model structure for a given type of hydrological system and a particular modelling task?” and “What is the appropriate parameter set within this structure to characterize the unique response features of a particular catchment?” (Wagener et al., 2004). It is also noted that firstly, simple models (in terms of number of parameters) could give as good a performance as complex models for many purposes, and secondly, many models have been developed, but only a limited number of them are used in reality (Wagener et al., 2004).

In this study, a number of popular methods for modelling rainfall runoff were considered. These methods have been assessed to see if they are suitable as tools for a decision support system in the Quang Nam situation. The considered models were the tank model, the unit hydrograph model (unit hydrograph with Clark’s technique in GIS (Usul and Yilma, 2004)) and a multiple regression model. As far as the tank model is concerned, it had too many parameters that needed to be calibrated. The tool for this model was developed and tested. However, with little or no local knowledge of the interception, infiltration, evaporation, surface and subsurface runoff characteristics of Quang Nam basin, the

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calibration of the model became too tricky. An automatic calibration procedure was also developed and tested however it does not give reasonable results. The situation was very much similar for the preliminary research into employing unit hydrograph method. This method depends on the knowledge about the flow velocities of fluid over different type of landuses (Usul and Yilma, 2004). This makes the calibration process tedious as a trial and error method was used to assign different values of Manning’s coefficients to landuse types has to be made. Although the model does not have as many parameters as the tank model, it does require some technical skills for calibration. With this in mind, after some preliminary study steps, this method was not considered for further development. In the context of Quang Nam basin, with the availability of rainfall and runoff time series data, the current hydrological monitoring system and the current capacity of the staff resource of the province, a multiple regression model is proposed as it is a simple model which is easy to implement in the decision support system. More importantly, the validation of the model against historical data showed that multiple regression gave good results, as will be discussed below.

5.2.. Regression model

The following discussion about multiple regression is an adapted from Haan (1997). Regression models include two parts, namely the predicted portion and residual portion. The predicted portion has the characteristic that can be attributed to all the observations which is considered as a group within a parametric framework. The residual portion is the difference between the observed and predicted values. The general form of a regression model is as follows:

𝑦𝑖 = 𝑓(𝑥𝑖, 𝛽) + 𝑒𝑖, 𝑖 = 1,2, … 𝑛 (5.1)

Where, n is the number of observations, yi is the ith observation, xi =(x1i, x2i, ..., xki) is the

predictor variable vector relating to yi, β = (β0, β1, ..., βp) is the parameter vector and ei is

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In the matrix form, the above model can be written as:

𝑌 = 𝑋𝛽 + 𝜀 _(5.2)

The estimation of the parameter vector β using least square method is derived as:

𝛽̂ = (𝑋𝑇𝑋)−1𝑋𝑇𝑌 (5.3)

The predicted model is:

𝑌̂ = 𝑋𝛽̂ (5.4)

so that the residual is given as:

𝑒 = 𝑌 − 𝑌̂ (5.5)