page_title: Hydrological model
section_title: Conceptual models
hierarchical_section_title: Hydrological model / Conceptual models
caption_attribution_description: English: Relation between reaction factor alpha of a non-linear reservoir model and runoff, Rogbom valley, Sierra Leone
context_page_description: A hydrologic model is a simplification of a real-world system that aids in understanding, predicting, and managing water resources. Both the flow and quality of water are commonly studied using hydrologic models.
context_section_description: Conceptual models represent hydrologic systems using physical concepts. The conceptual model is used as the starting point for defining the important model components. The relationships between model components are then specified using algebraic equations, ordinary or partial differential equations, or integral equations. The model is then solved using analytical or numerical procedures.
  Example 1
  The linear-reservoir model (or Nash Model) is widely used for rainfall-runoff analysis. The model uses a cascade of linear reservoirs along with a constant first-order storage coefficient, K, to predict the outflow from each reservoir (which is then used as the input to the next in the series).
  The model combines continuity and storage-discharge equations, which yields an ordinary differential equation that describes outflow from each reservoir. The continuity equation for tank models is:
  which indicates that the change in storage over time is the difference between inflows and outflows. The storage storage-discharge relationship is:
  where K is a constant that indicates how quickly the reservoir drains; a smaller value indicates more rapid outflow. Combining these two equation yields
  and has the solution:
  Example 2
  Instead of using a series of linear reservoirs, also the model of a non-linear reservoir can be used.
  In such a model the constant K in the above equation, that may also be called reaction factor, needs to be replaced by another symbol, say α (Alpha), to indicate the dependence of this factor on storage (S) and discharge (q).
  In the left figure the relation is quadratic:
  α = 0.0123 q² + 0.138 q - 0.112
caption: The reaction factor Alpha increases with increasing discharge.[34]
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