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encountered, such as Darcy-Richards concerning underground drainage. These models are complex and may require spatialized information (2D or 3D grid system), robust numerical schemes, and the assignment of physical parameters for each physical unit (each cell of the grid). A classical model in hydrology is the European MIKE SHE, which is an integrated modeling framework to simulate all components of the land phase of the hydrologic cycle (surface water and groundwater). Another important classification of deterministic models in hydrology is that related to the degree of complexity concerning the physical measurements of the basin or the area to be studied. These can be divided into global or distributed models. Global models generally consider the studied area as a whole, a total; all the parameters and characteristics are similar, but they fail to explain all the processes that occur within the studied area. However, they properly represent the physical process in one particular point. The distributed and semi-distributed models can represent the processes that take place throughout the studied area, but their operation is diďŹƒcult and requires a large amount of data as well as parameters (usually physics-based models). Within the deterministic models, there are other series of classifications; those that analyze the evolution of the physical process: linear models (for example, flow as a direct consequence of precipitation) and nonlinear models (such as flow as a nondirect consequence of precipitation, use of fictitious reservoirs). These are analyzed by the variation of physical parameters in time (seasonal and nonseasonal) and will not be addressed in this analysis because their characteristics may be within the models already described above. Stochastic models: As noted, stochastic models give several outputs for one input in the model. These models are used to simulate complex physical processes that appear to be directed by randomness. The simplest examples of stochastic models are time series in which the variables given at a particular moment are according to their previous values and random error. In this case, the function that unites the values of the variable at dierent times are deterministic and the error is stochastic. The classical examples are the Markov chains, ARMA (Auto Regressive and Moving Average), etc. Figure A4.1 shows a descriptive picture of the dierent types of existing models for hydrological modeling.
Figure A4.1. Simplified structure of the models
Source: Authors.