A model is defined as any device that represents an approximation of a field situation (Anderson and Woessner, 2002). It consists of a set of simultaneous equations or a logical set of operations contained within a computer program. Models have parameters, which are numerical measures of a property or characteristics that are constant under specified conditions (Wheater, 2008). Different model types or source codes are available and several attempts were made to classify hydrological models
(e.g. Fleming, 1975; Singh, 1995; Refsgaard, 1996; Wheater, 2008). By reviewing the available literature, it was found that most of the models‟ classifications are based on the hydrological process description, but another classification was found, based on the technological level of the models, as given by Abbott et al. (1991). A summary of model classification is given for both classification types, with more emphasis on model classification with respect to hydrological process description due to its relevance for this research.
3.2.1 Model classification according to hydrological process description Hydrological models can be classified to be deterministic or stochastic; in the deterministic approach, the models are grouped according to whether they give a lumped or a distributed description of the considered area and whether the description of the hydrological processes is empirical (black box), conceptual (grey box), or physically based (white box). Models based on stochastic approach are derived from a time series analysis of historical records, and then the model can be used to generate a long-term hypothetical sequence of events with the same statistical properties as the historical records. Today, a joint stochastic-deterministic methodology is common, presenting a useful framework for addressing some of the fundamental problems in hydrology such as taking spatial variability into account and assessing uncertainties in modelling. The given classification is schematic and many model codes do not fit exactly into one given class. The following classification is based on Refsgaard (1996) where an excellent and detailed description of all these classes is given.
3.2.1.1 Deterministic models
In deterministic models, a set of input values always gives the same output values.
These models are classified into three groups: empirical, lumped-conceptual, and distributed-physically based (Fig. 3.1). The empirical models use mathematical equations, which are based on analysis of concurrent input and output time series not from the physical processes in the catchment area. Examples of empirical models used in hydrological modelling are the Constrained Linear Systems (CLS) models (Todini and Wallis, 1977) and the Antecedent Precipitation Index (API) model (WMO, 1994).
A model is said to be lumped if the parameters, inputs and outputs, are spatially averaged to one value for the whole modeled catchment area; a typical example of lumped-conceptual model group is the Stanford modelling system (Crawford and Linsley, 1966).
In the distributed-physically based model, the parameters, inputs, and outputs vary spatially. Typical examples of models using this approach are the IHDM model (Beven et al., 1987), the THALES model (Grayson et al., 1992) and the MIKE SHE model (Refsgaard and Storm, 1995).
The physically based models are based on the best available understanding of the physics of hydrological processes and on a continuum representation of catchment processes. The equations of motion of the constituent processes are solved numerically using a grid, which is usually discretized relatively crudely in catchment-scale applications (Wheater, 2008). The physically based distributed models are
thought to have an advantage over simpler black box or even lumped physically based models, due to their use of spatially distributed parameters which have a physical significance (Bathurst, 1986). This type of model has been developed from a need to analyze and solve specific hydrological problems often required in multi-objective and multi decision management investigations (Storm and Refsgaard, 1996).
Fig. 3.1: Classification of hydrological models according to process description (modified from Refsgaard, 1996).
3.2.1.2 Stochastic models
A model is classified as stochastic if, due to random components, a set of input values do not necessarily produce the same output values. The stochastic model is based on probability laws which seek to account for random behavior which cannot be explained deterministically. For example, precipitation exhibits highly random behavior when observed as a function of time and space, but for long term predictions the probability theory and probability laws provide an appropriate frame work (O‟Connell, 2000). The technique of generating several synthetic series with identical statistical properties based on historical records is called the Monte Carlo technique (Refsgaard, 1996). A description of stochastic time series models is given by Salas (1992). Several rainfall-runoff models are based on the stochastic time series approach (e.g. Freeze, 1980; Storm et al., 1988).
3.2.2 Model classification according to technological level
This type of classification, which has been given by Abbott et al. (1991), is based on the level of technology involved in the models (i.e. the level of sophistication).
Models can be seen as falling into one of five generational categories:
Hydrological Simulation Models
Deterministic Stochastic
Empirical (Black box)
Distributed Physically-based
(White box) Lumped
Conceptual (Grey box)
Joint Stochastic and Deterministic
First generation (Computerized Formula): appeared in the 1950s, and was characterized by the use of the first computers as calculation devices for analytical expressions.
Second generation (One-off Numerical Models): appeared in the 1960s;
models of this generation are characterized as being constructed, developed, and applied by mostly universities or research institutes to usually solve one specific problem. Utilization was restricted to the developers of the code.
Third generation (Generalized Numerical Modelling System): a development of the second generation due to the problem solving versatility of that code. In hydrology, the first distributed physically-based systems were made in the beginning of the 1980s, while the much simpler lumped conceptual systems appeared in the 1960s (Refsgaard, 1996).
Fourth generation (The Industrial User-friendly Software Product): the products of this generation are user friendly software which can be applied by professional engineers and scientists. The models of this generation differ from the third generation by being fully menu-based, with interactive execution and online help menus; also they provide comprehensive error message and automatic checks for obviously erroneous input data. These models have powerful graphics facilities, are much better documented and proven, and they are more easily transferable and installable.
Fifth generation (Intelligent Modelling System): designed for technically-skilled but non-expert users and they merge into hydroinformatics tools, generally, such as diagnostic and real time control systems and management support systems.
The fourth generation systems have no demands on user experience in computer systems or numerical techniques but they require that the user has an experience in modelling. Most of the present models belong to the fourth generation while the fifth generation systems are still in the experimental stage, except for real-time control applications used in urban drainage systems (Refsgaard, 1996).