As briefly mentioned in the introduction, physically-based models are those that solve differential equations that represent different physical processes of water motion by numerical approximation in space and/or time. Examples of processes where such approaches are applied are: water quantity and quality, flood routing, rainfall-runoff and groundwater flow.

A common distinction between different kinds of physically based models is with respect to the number of spatial dimensions used for the mathematical representation of the modelled physical processes. Therefore models are: zero-dimensional (or lumped conceptual) where all spatial dimensions are ignored and only temporal variations are considered (treating water system elements as lumped units, without spatial representation); one-dimensional models (1-D) used for example in river systems modelling, where the river is considered as a 1-D spatial element; two-dimensional (2-D, used in flood analysis, or analysis of groundwater systems; and three –dimensional ones (3-D), used for detailed analysis of lake systems, or three-dimensional flow around hydraulic structures.

These different modelling approaches are commonly associated with certain application areas. Hydrological models, for example, frequently use 0-D and simplified versions of 1-D approaches. Similarly, water allocation models (also mainly use 0-D. Models of urban water systems, such as water distribution and drainage networks are commonly using 1-D approaches, while hydraulic models of rivers and floodplains are combining 1-D and 2-D approaches. Detailed analysis of deep lakes is carried out with 3-D models. Water quality modelling can be associated with any of these models, however, the complexity representation of the water quality parameters and their interactions is different for 0-D,1-D, 2-D or 3-D models.

Mathematical representation of the physical processes also depends on the type of flow that is being considered, such as pressurized free surface or groundwater flow.

Nowadays there are many physically based modelling systems available. These are software packages that incorporate generic algorithms for solving particular mathematical equations, applicable for a given application domain. By introducing data for a specific case, such as boundary conditions, parameters, geometry, etc. the modelling system can be used to instantiate a model for a particular situation (i.e. river, catchment, aquifer system, ) depending on the application. The availability of modelling systems has introduced different business models in relation to delivery of water modelling software products and services, which are continuously evolving. Current business model trends are towards deploying instantiated models and even modelling tools on the Internet, which will increase their accessibility and usage for different water management tasks.

Examples of well-known European modelling systems are: MIKE ZERO modelling suite developed by Danish Hydraulic Institute (DHI) from Denmark s; Delft3D and Sobek released by Deltares, from the Netherlands; and Infoworks of Wallingford Software from UK. Elsewhere, like in USAmany modelling systems are developed and maintained by different federal agencies, such as United States Geological Survey ( USGS); US Army Corps of Engineers (USACE), Environmental Protection Agency (EPA), etc.

Frequently newly released modelling systems are freely available, and some do lack sophisticated user interfaces for pre- and post-processing of data and modelling results. Different private companies develop such components around the freely available modelling systems and offer them as commercial products and services (e.g. Bentley, Aquaveo). In addition, many academic centres, such as universities and research institutes maintain freely available academic software, which sometimes develops into larger open source projects for water modelling software.

The primary advantage of physically-based models is that they contain representations of the physical system and can be used for modelling change that may be introduced in such systems. Therefore, they are indispensable support for design and planning tasks. Their disadvantages may be large data requirements for being set up and sometimes long computational times.

Hence sophisticated physically-based models may not be needed for regular operational management tasks. Another category of water models, named ‘data-driven models’ has recently emerged as an alternative to-, and often complementary use with physically based models.

Available software tools

Among the tools to support hydrological modelling and decision-making, Geographical Information System (GIS) is highly regarded as an important instrument for data management. For example, even when surface water and groundwater are modelled separately, GIS can support integration between them [Facchi, 2004]. For example, modelling software like Mike BASIN is selected often by different authors to model surface water. Groundwater models are also available are available in the ASM software. When both surface water and groundwater need to be modelled together, both for quantity and quality evaluations, such tools (actually, the complexity comes from the integration of the models these two provide) can be by means of a GIS, to support efficient data management. Such an approach was demonstrated in [Jain, 2004], where authors developed a process oriented distributed rainfall runoff model, which used a GIS to generate model inputs in terms of land use, slope, soil and rainfall. This allowed the model to handle catchment heterogeneity.

Similarly, the GIS software ArcView, developed by ESRI, combines several capabilities for mapping systems along with the ability to analyse geographic locations and the information linked to those locations. A powerful feature of ArcView GIS is the ability to carry out mathematical and logical operations on spatial data. Furthermore, tabular data from Arcview dBASE files can be created or manipulated using Microsoft Excel, which is useful in facilitating the integration of ArcView with other software.

But the power of such modelling tools can really be put to use when combined. As a pioneer case study, authors in [Ireson] proposed a methodology for loosely-coupling the MIKE BASIN with the ASM provided water models, and demonstrate a series of what-if scenarios for the effect of dams on the groundwater.

MIKE

MIKE BASIN, developed by DHI software, is an extension of ArcView, which uses GIS information as a basis of a water resources evaluation. Crucially, MIKE BASIN adds to ArcView the capability to deal with temporal data, in addition to the spatial data stored in the GIS. MIKE BASIN is a water resources management tool, which is based on the basin-wide representation of water availability. Rivers and their main tributaries are represented mathematically by a network of branches and nodes. Nodes are point locations, where it is assumed that water enters or leaves the network through extractions, return flow and runoff. These may be confluences, diversions, locations where certain water activities occur (such as water offtake points for irrigation or a water supply), or important locations where model results are required. Rainfall-runoff modelling can be carried out in MIKE BASIN using the NAM model, a lumped, conceptual rainfall-runoff model suitable for modelling rain-fall-run-off processes on the catchment scale. This can be used to simulate overland water flows, for example.

ASM

ASM, Aquifer Simulation Model for Microsoft Windows, is a complete two-dimensional groundwater flow and transport model. ASM include the instruments to model either confined and unconfined aquifers. For modelling an aquifer as a confined aquifer, the governing equations are based on transmissivity parameters, which are fixed because the saturated depth is fixed (in reality, when the water level in the aquifer drops below the confining layer, the saturated depth of the aquifer decreases, as does the transmissivity; thus, strictly speaking, the model is fundamentally flawed in this manner). For a steady-state model, the groundwater levels do not change once the solution has converged. Therefore, in such a model the transmissivity is effectively fixed, meaning the basic assumptions are still valid, however the data used to define the model should be based on measured or calibrated transmissivity and not on measured hydraulic conductivity. This also means that only steady-state analysis can be carried out with this model.