A hydrologic model is a simplification of a real-world system (e.g., surface water, soil water, wetland, groundwater, estuary) that aids in understanding, predicting, and managing water resources. Both the flow and quality of water are commonly studied using hydrologic models.
Analog models
Prior to the advent of computer models, hydrologic modeling used analog models to simulate flow and transport systems. Unlike mathematical models that use equations to describe, predict, and manage hydrologic systems, analog models use non-mathematical approaches to simulate hydrology.
Two general categories of analog models are common; scale analogs that use miniaturized versions of the physical system and process analogs that use comparable physics (e.g., electricity, heat, diffusion) to mimic the system of interest.
Scale analogs
Scale models offer a useful approximation of physical or chemical processes at a size that allows for greater ease of visualization. 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). Yet, maintaining some properties at their natural values can lead to erroneous predictions. Properties such as viscosity, friction, and surface area must be adjusted to maintain appropriate flow and transport behavior. This usually involves matching dimensionless ratios (e.g., Reynolds number, Froude number).
Groundwater flow can be visualized using a scale model built of acrylic and filled with sand, silt, and clay. Water and tracer dye may be pumped through this system to represent the flow of the simulated groundwater. Some physical aquifer models are between two and three dimensions, with simplified boundary conditions simulated using pumps and barriers.
Process analogs
Process analogs are used in hydrology to represent fluid flow using the similarity between Darcy's Law, Ohms Law, Fourier's Law, and Fick's Law. The analogs to fluid flow are the flux of electricity, heat, and solutes, respectively. The corresponding analogs to fluid potential are voltage, temperature, and solute concentration (or chemical potential). The analogs to hydraulic conductivity are electrical conductivity, thermal conductivity, and the solute diffusion coefficient.
An early process analog model was an electrical network model of an aquifer composed of resistors in a grid. Voltages were assigned along the outer boundary, and then measured within the domain. Electrical conductivity paper can also be used instead of resistors.
Statistical models
Statistical models are a type of mathematical model that are commonly used in hydrology to describe data, as well as relationships between data. Using statistical methods, hydrologists develop empirical relationships between observed variables, find trends in historical data, or forecast probable storm or drought events.
Moments
Statistical moments (e.g., mean, standard deviation, skewness, kurtosis) are used to describe the information content of data. These moments can then be used to determine an appropriate frequency distribution, which can then be used as a probability model. Two common techniques include L-moment ratios and Moment-Ratio Diagrams.
The frequency of extremal events, such as severe droughts and storms, often requires the use of distributions that focus on the tail of the distribution, rather than the data nearest the mean. These techniques, collectively known as extreme value analysis, provide a methodology for identifying the likelihood and uncertainty of extreme events. Examples of extreme value distributions include the Gumbel, Pearson, and Generalized Extreme Value. The standard method for determining peak discharge uses the log-Pearson Type III (log-gamma) distribution and observed annual flow peaks.
Correlation analysis
The degree and nature of correlation may be quantified, by using a method such as the Pearson correlation coefficient, autocorrelation, or the T-test. The degree of randomness or uncertainty in the model may also be estimated using stochastics, or residual analysis. These techniques may be used in the identification of flood dynamics, storm characterization, and groundwater flow in karst systems.