One-Dimensional Lake Stratification


Simple Dynamic Estimation of Reservoir Stratification


The purpose of this model is to demonstrate estimation of dynamic lake stratification by applying the one-dimensional stratification method of Tchobanoglous et al. (1987) in a simple reservoir model. Stratification is determined dynamically in the sense that the determination of whether the reservoir is stratified or not can change over time. Reservoir stratification is determined based on the dimensionless Densimetric Froude (NDF) number which essentially provides an inverse Richardson number. NDF provides the ratio of a characteristic velocity (u), or kinematic energy - inertial forces, to a characteristic wave velocity (c), or potenial energy - gravitational forces. When u is small relative to c and NDF is small (less than 0.1 in this case), then there is little kinetic energy available for mixing and reservoir is assumed to be stratified. When u is large relative to c and NDF is greater than 1 then there is kinetic energy available for mixing and the reservoir is assumed to be well mixed (i.e. un-stratified). In between (0.1 < NDF < 1.0), the reservoir is assumed to be weakly stratified (i.e. weakly mixed).

The model simulates a reservoir, over 24 hours, that is filled using an allocation on a river to meet a fill target. Meanwhile, a water demand based on an assumed amount of irrigated land area is applied and water is delivered and the reservoir is drained. Along side the dynamics of this reservoir, lake stratification is calculated on each timestep. At the end of the run, the number of days the reservoir exists within each type of stratification (strong, weak, or fully mixed) is presented as percentages of total simulation duration in the plot called, "Stratification_Percent_Time". The estimation of the degree of stratification is dynamic because the characteristic velocity (u) which is assumed to be reservoir outflow varies over time during the simulation. The total depth (d) and the density of water at the reservoir surface also vary over time as the reservoir water level changes and due to diurnal heating. Water temperature at the bottom of the reservoir is assumed to be fixed and water density is assumed to be dependent only on temperature.


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