Summary of key issues:
|Description||Characterisation of the estuary system or estuary processes into manageable stand alone mathematical equations.|
|Temporal applicability||Short term (several tides) to long term (100 years)|
|Spatial applicability||Whole estuary or large areas of the estuary|
|Links with other tools||
|Data sources||Sources vary enormously depending on the type of analytical equation|
|Necessary software tools / skills||
|Limitations||It can be necessary to consider the mathematics of the method in detail to understand whether a particular analytical method can reliably be applied to a given estuary system.|
Analytical solutions are a group of mathematical expressions, often derived from basic physical principles, but usually resulting from a simplification of estuary systems that can be utilised to gain insight into the functioning and potential changes within an estuary system.
Overview of technique
Analytical solutions exist for a diverse range of physical processes and mechanisms encountered within estuarine environments. These include tidal propagation and current flow, residual circulation, saline intrusion, wind-wave generation, wave propagation and evolution, sediment transport, flocculation and contaminant mixing.
The role of analytical solutions is to simplify the estuary system or the physical process in question into something more tangible and useable. As a result, the complex and often random nature of natural systems, which obscures the underlying process, can be removed to reveal the first order relationships associated with the system or physical process. These relationships then allow a straightforward evaluation of the impact of changes to the underlying drivers in the system or physical process to be evaluated. Usually this simplification enables changes to estuary systems to be evaluated in a qualitative manner, but in appropriate circumstances analytical solutions can provide quantitative estimates. In such circumstances the simplified nature of analytical solutions typically results in tools which are quick to use and require only a calculator or spreadsheet to implement.
In order to derive the analytical solutions, a number of simplifying assumptions normally have to be made regarding the estuary system or physical process. The determination of these assumptions requires judgement and experience to assess whether the analytical solution can be applied because the assumptions must be appropriate for a given situation.
The scope of analytical methods that could be considered is wide and therefore it is has been necessary to limit those considered here to those that featured in the Estuaries Research Programme Phase 1 study (EMPHASYS, 2000) and the Phase 2 EstProc study (EstProc Consortium, 2006), which include:
- Tidal flow;
- Residual current profiles and saline intrusion;
- Residual sediment transport; and
- Suspended sediment concentration profiles.
For each of these an introduction to the theory is presented and any applicable approaches, followed by conclusions. This is in turn followed by best practice advice for each.