 # Deterministic model (deductive) hydrological modelling

## Definition

If the chance of occurrence of the variables involved in such a process is ignored and the model is considered to follow a definite law of certainty but not any law of probability, the process and its model are described as deterministic. For example, the conventional routing of flood flow through a reservoir is a deterministic process and the mathematical formulation of the unit-hydograph theory is a deterministic model.

## Methodology

Related to deterministic models there are essentially three categories of hydrologic forecasting models:

### Black box or system theoretical models:

Any mathematical model whose inputs are expressed as random variables, and whose output is a distribution of possible results are associated with stochastic models.

In black box models, the emphasis is placed on identifying a relationship between input and output of the model, without worrying explicitly about the physical mechanisms of converting. A black box model does not attempt in any way to represent the process occurring within the catchment, not even in a simplified manner.

A classic example of this type of model is the unit hydrograph often used for small basins.

### Physically-base distributed models:

A mathematical model is deterministic if the output is determined by the mathematical form of its equations and by the selection of a single value for each input parameter. In case of hydrological models this category of models is for example characterised by a simplified but plausible representation of the main components of the rain-discharge process.

In general, the internal description of the various subprocesses are modelled attempting to represent, in a simplified way, the known physical processes. These models ensures the conservation between precipitation, discharge and storage volume in the various reservoirs. They are based on physical knowledge of the watershed and use physically based equations to describe these processes. With this type of model, continuity, energy and time equations are used to represent the water displacement in the watershed. This representation leads to a system of partial differential equations that must be solved numerically.

### Detailed model:

Based on the physical interrelations between initial conditions and output values (i.e. rainfall runoff models). This model is subdivided in:

• Short term model: The simulation of rainfall runoff processes is limited to flood simulation.
• Long term simulation: Rainfall runoff model are conceptualised for the calculation over longer period (water balance models, low water models) Headers and keywords Page content

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Module Flood modelling TUHH - - - 