Hydrological model
Scale models offer a useful approximation of physical or chemical processes at a size that allows for greater ease of visualization.
[1] The model may be created in one (core, column), two (plan, profile), or three dimensions, and can be designed to represent a variety of specific initial and boundary conditions as needed to answer a question.
Scale models commonly use physical properties that are similar to their natural counterparts (e.g., gravity, temperature).
[2] Properties such as viscosity, friction, and surface area must be adjusted to maintain appropriate flow and transport behavior.
Groundwater flow can be visualized using a scale model built of acrylic and filled with sand, silt, and clay.
Some physical aquifer models are between two and three dimensions, with simplified boundary conditions simulated using pumps and barriers.
[8] Using statistical methods, hydrologists develop empirical relationships between observed variables,[9] find trends in historical data,[10] or forecast probable storm or drought events.
[21] These techniques may be used in the identification of flood dynamics,[22][23] storm characterization,[24][25] and groundwater flow in karst systems.
Within a temporal dataset, event frequencies, trends, and comparisons may be made by using the statistical techniques of time series analysis.
Markov Chains were first used to model rainfall event length in days in 1976,[32] and continues to be used for flood risk assessment and dam management.
Conceptual models are commonly used to represent the important components (e.g., features, events, and processes) that relate hydrologic inputs to outputs.
The conceptual model would then specify the important watershed features (e.g., land use, land cover, soils, subsoils, geology, wetlands, lakes), atmospheric exchanges (e.g., precipitation, evapotranspiration), human uses (e.g., agricultural, municipal, industrial, navigation, thermo- and hydro-electric power generation), flow processes (e.g., overland, interflow, baseflow, channel flow), transport processes (e.g., sediments, nutrients, pathogens), and events (e.g., low-, flood-, and mean-flow conditions).
In the left figure the relation is quadratic: Governing equations are used to mathematically define the behavior of the system.
Examples of governing equations include: Manning's equation is an algebraic equation that predicts stream velocity as a function of channel roughness, the hydraulic radius, and the channel slope: Darcy's law describes steady, one-dimensional groundwater flow using the hydraulic conductivity and the hydraulic gradient: Groundwater flow equation describes time-varying, multidimensional groundwater flow using the aquifer transmissivity and storativity: Advection-Dispersion equation describes solute movement in steady, one-dimensional flow using the solute dispersion coefficient and the groundwater velocity: Poiseuille's law describes laminar, steady, one-dimensional fluid flow using the shear stress: Cauchy's integral is an integral method for solving boundary value problems: Exact solutions for algebraic, differential, and integral equations can often be found using specified boundary conditions and simplifying assumptions.
Laplace and Fourier transform methods are widely used to find analytic solutions to differential and integral equations.
Many real-world mathematical models are too complex to meet the simplifying assumptions required for an analytic solution.
These parameters can be obtained using laboratory and field studies, or estimated by finding the best correspondence between observed and modelled behavior.
