A variety of model structures are available, suiting different modeling purposes. A commonly acknowledged classification scheme for hydrological models is provided by Becker & Serban (1990). The authors distinguish models according to its degree of causality and its spatial representation (see Figure 4-2). A first rough divide can be made between stochastic and deterministic models.
Figure 4-2: Main categories of hydrological models and their areal discretization schemes (modified after Becker & Serban 1990)
A model is called stochastic, when probabilistic laws are being used and stochastic elements, with known or estimated distributions, occur in the model. Therefore ranges of results are produced or model runs produce different output. This model type is not further explained here. A model is called deterministic when a given input always results in the same output.
The relations between input and output may be described using physical laws (white box or physically-based), simplifications of these laws (grey-box or conceptual10) or empirical relationships (black box). The degree of process understanding associated with the model development should be corresponding to the modeling purpose (see previous section).
10 In hydrological modeling “conceptual model” is an ambiguous term that refers to a stage in model development (previous section 4.1) and a specific type of model structure (this section). The ambiguity remains unresolved for this work; hence the appropriate connotation is determined by the context.
Obviously these different model types suit different tasks and varying spatial discretization can be associated with them. The following paragraphs provide general ideas of scales, model complexity and spatial regionalization schemes.
4.1.1.1 Scales
Characteristic space and time scales are associated with different hydrological processes (Blöschl & Sivapalan 1995). While shifting scales new processes might gain importance (emergence). For instance real-time flood-monitoring requires models that operate on sub-daily time steps, and focus on surface flow and channel processes (lower left center of Figure 4-3), whereas irrigation managers might use models operating on monthly time-scales, focusing on snow-melt or groundwater dynamics (top center of Figure 4-3). These requirements demand different models, with different simplifications.
Figure 4-3: Hydrological processes at a range of characteristic space-time scales (Blöschl & Sivapalan 1995)
A modeling challenge associated with scales is that required data is available on different scales only (Beven 1995; Wood et al. 1988). As exemplary variables meteorological data can be considered. Generally measured climate data is site-specific, whereas modeled climate data refers to grid cells larger than 100 km². The same accounts to parameters that, though derived from local measurements, represent areal entities (Herbst et al. 2006).
4.1.1.2 Model complexity
A general trend in modeling is to use the most sophisticated scheme that can be practically applied, based on the assumption that, the more processes a model includes the better its results are (Bates & De Roo 2000). However the authors argue that ultimately the best model will be the simplest one that provides the information required by the user whilst reasonably fitting the available data. Grayson & Blöschl (2001) point out that model complexity needs to match the data available. Otherwise model parameters cannot be identified properly (model complexity > data availability) or the model is not able to fully exploit the data (data availability > model complexity, Figure 4-4).
Figure 4-4: Data availability, model complexity and model performance (Grayson & Blöschl 2001)
Some input elements have a reduced or insignificant influence over the output; only the sensitive relations between input and output must be evaluated. From a practical point of view, this means that only a relatively reduced number of input elements are considered as proper input, being linked to the output through strong causal dependencies; the remaining input elements are neglected or considered perturbations, which produce deviations (or noise) from the system's deterministic behavior. If the deviations are too large, one should widen the focus of the investigation, as one or more significant inputs may have been neglected.
Following this approach, the optimum model complexity can be obtained.
4.1.1.3 Spatial discretization
It has been shown in section 4.1.1 that the model structure is associated with its spatial representation. Therefore a variety of spatial representations exist. Several distributed hydrological models are based on regular grids, e.g. MIKESHE (Abbott et al. 1986a; Abbott et al. 1986b), ECOMAG (Motovilov et al. 1999), and TOPKAPI (Ciarapica & Todini 2002).
The choice of the grid size is not always dependent on the processes that are represented, but rather a result of available data resolution (see the previous section 4.1.1.2 for associated problems). Instead of using square elements, some discretizations of irregular geometry are proposed as well: iso-contours of elevation in TOPOG (Vertessy et al. 1993) or Triangular Irregular Networks in tRIBS (Vivoni et al. 2005). The latter solutions pronounce already aspects of computational efficiency and “similarity” of mesh units, in terms of elevation, aspect, etc. Hydrological similarity of model units is a prerequisite for spatial aggregation beyond grid or mesh-size. Beven & Kirkby (1979) used the topographic index to derive units of hydrological similarity in TOPMODEL.
The Representative Elementary Area concept (REA; Wood et al. 1988) pronounces the existence of characteristic spatial scales for different hydrological processes. Therefore specific features can be assumed to be distributed statistically beyond related thresholds. This approach has been further developed by Reggiani et al. (1998), who propose the use of Representative Elementary Watersheds (REW), self-similar modeling units that are characterized by the same parameter sets, independent of the required scale (i.e., from the drainage area of a stream to that of a rill). Anyhow in the latter case relationships and fluxes between REWs have to be described for every scale considered.
Flügel (1995) propose to define Hydrological Response Units (HRU), based on topography, soils, geology, precipitation characteristics and land cover. SWAT utilizes HRUs based on soils, geology and land cover (Arnold et al. 1993) and most recently slope (Winchell et al.
2007). One of the drawbacks of the HRU mapping is the merging of smaller units into larger ones by applying thresholds or smoothing filters. The resulting loss of information might lead to the overlooking of major hydrological processes that are localized on small units, such as return flow above rock outcrops, transpiration of riparian vegetation, etc. This shortcoming is partly overcome by the development of pre-processing routines allowing to consider special land cover types or soils, even if their spatial extent is below the chosen thresholds (Di Luzio et al. 2004).