Formulae for pressure gradients in one‐dimensional lake models

Formulae for barotropic and baroclinic pressure gradients, suitable for one-dimensional lake models, are derived and explored. The derivation is based on the equation for free standing oscillations and a continuity relation. The formulae, which are easy to derive and use, give the correct external and internal seiche frequencies for nonrotating, rectangular one- or two-layered basins of constant depth. When applied to situations with continuous stratification, further assumptions need to be introduced. These are discussed in the paper. Applications to a laboratory experiment, dealing with wind-induced entrainment, show that pressure gradients for the entrainment process are significant and that the pressure formulae derived capture this effect. The formulae are also used in combination with a one-dimensional lake model. Comparisons with field measurements of the seasonal stratification show that the inclusion of pressure gradients improves the predictive capabilities of the lake model.