Criteria for selection of spatial dimension in the application of one- and two-dimensional water quality models

A critical aspect of modelling water quality in lakes and reservoirs is to select a model with a spatial representation that is appropriate for the dominant mixing processes and the observed variation in water quality variables. One-dimensional modelling is frequently applied to small-to-medium size lakes and reservoirs to encompass variations that are most pronounced in the vertical as a result of seasonal or permanent density stratification. Two- and three-dimensional models are generally applied to larger water bodies where both horizontal and vertical variations are important. Horizontal variations may result from the local effects of inflows and outflows, basin scale seiching and wind mixing. Increased dimensional capabilities in water quality models produce a large increase in computational time and may therefore impose severe constraints on the length of the simulation. This problem is most frequently averted by increasing the time step, which in itself may introduce problems associated with numerical diffusion. Therefore when longer simulations of water quality in a lake are required, as is often the case for management applications, it is desirable to select a model with the least spatial dimension required to adequately encompass the observed variation in water quality variables and the most important mixing processes. This study proposes a set of criteria that can be used a priori to select the appropriate dimensional representation when applying a water quality model to a lake. The critical factors that influence the application of a one- or two-dimensional model are the size of the lake, the volume of the inflows and the settling velocity of particulates in the inflows.