# What is the model of a groundwater flow (hydraulic model)?

Generally speaking, models are a simplified functional representation of a real physical system.

As regards hydraulic models, the definition could be refined to read that a hydraulic model is a general simplified functional representation of a real hydrogeological system that is used to analyse the behaviour of the system as a whole, including its partial components.

The meaning of the term “model” varies and depends on the context it is used in. The majority of models belong to one of the following categories:

- qualitative description of processes taking place in the system, e.g. in the form of a diagram, verbal description
- simplified physical representation of a system, such as physical models made of equivalent materials, electric analogues, laboratory experiments, etc.
- mathematical representation of a physical system.

The text below deals only with the third category of models which can be expressed in mathematical form and processed via computer programs.

Every study of various aspects of hydrogeological process, which has ambitions of being more than a pure collection and tabulating of data, always encompasses a modelling in the broadest sense of the word. At the very beginning, the hydrogeologist conceives an idea of how the very system functions. This construct is usually referred to as a **mental model**. The mental model is followed by a so-called **conceptual model** which is a translation of the mental model into a form that is communicable to the experts. This tends to be a more accurate description of the system which may come in different forms, typically graphic – charts, block diagrams, cross section views, maps, etc. accompanied by relevant captions. The conceptual model typically incorporates a determination and geometrisation of hydrogeological units (aquifers, aquitards or aquicludes), qualified estimates of their hydraulic parameters, qualitative descriptions of boundary conditions, definitions of sources and faults, or outlined water balance of the area concerned. The last step is the **conversion of the conceptual model into the mathematical model**, which is associated with a spatial and time discretisation of the area concerned.

**Mathematical modelling** is becoming an increasingly more important and effective tool for exploration of hydrogeological processes as it allows an approximation of hydrogeological and other processes in their interaction based on the data available. There are two basic approaches that can be defined within the mathematical modelling: (1) direct modelling and (2) inverse modelling.

In direct modelling, the model parameters (e.g. hydraulic properties of the aquifer) are determined and levels and flow rates subsequently calculated on the basis of these parameters. This is made in spite of the fact that for the majority of modelled systems there is far more data about levels, flow rates or directions of flow available than the parameters of the environment being modelled. Typically, the input parameters are edited in the course of calibration using the trial-and-error method. This process usually leads to an acceptable calibration error between the observation and simulation. Yet it is more time-consuming and may not always find the best correspondence between the field data and calculated data, let alone the quantification of uncertainty in values of the estimated parameters, and/or the model results.

With the increasing capabilities of computer technology, the inverse modelling is used more frequently. It consists in repeated, systematic and automatic editing of the model parameters (hydraulic properties of the model layers or the boundary conditions, groundwater recharge, etc.) so that the resultant flow pattern suits the field observation (groundwater levels in wells, flow rates in water streams, etc.) as much as possible.